Staff Selection Commission Mathematics - Percentage (1999-2017)

TYPE–II

Q.1

If x is less than y by 25% then y exceed x by :

33\(\frac{1}{3}\)%

25%

75%

66\(\frac{2}{3}\)%

Ans .

33\(\frac{1}{3}\)%

Explanation :
Let y be 100.

∴ x = 75

∴ Required percentage = \(\frac{25 \times 100}{75}\) = \(\frac{100}{3}\) = 33\(\frac{1}{3}\)%

Q.2

. If x is 10% more than y, then by what per cent is y less than x ?

9\(\frac{1}{11}\)%

7\(\frac{1}{11}\)%

8\(\frac{1}{11}\)%

10\(\frac{1}{11}\)%

Ans .

9\(\frac{1}{11}\)%

Explanation :
Required per cent decrease = \(\frac{10}{100+10} \times 100\) = \(\frac{10}{110} \times 100\) = 9\(\frac{1}{11}\)%

Q.3

. If A’s height is 10% more than B’s height, by how much per cent less is B’s height than that of A ?

10%

10\(\frac{1}{9}\)%

10\(\frac{1}{11}\)%

9\(\frac{1}{11}\)%

Ans .

9\(\frac{1}{11}\)%

Explanation :
If the first value is r % more than

the second value, then second

is\(\frac{r}{100+r} \times 100\)%less than the first value.

∴ Required percentage =\(\frac{1}{110} \times 100\) = \(\frac{100}{11}\) = 9\(\frac{1}{11}\)%

Q.4

. B got 20% marks less than A. What per cent marks did A got more than B ?

20%

25%

12%

80%

Ans .

25%

Explanation :
Required percentage = \( \frac{20}{100-20} \times\ 100 \) = 25%

Q.5

If x earns 25% more than y. What percent less does y earn than x ?

16%

10%

20%

25%

Ans .

20%

Explanation :
Required percentage = \(\frac{25}{100 +25} \times 100\) = 20%

Q.6

The difference of two numbers is 20% of the larger number. If the smaller number is 20, the larger number is :

Ans .

Explanation :
Let the larger number be x

\(→\) According to question,

x – 20 = 20% of x

or, x – 20 =\(\frac{x}{5}\)

or, x – \(\frac{x}{5}\) = 20

or, 5x – x = 20 × 5

or, 4x = 20 × 5

\(→\) x = 5 × 5 = 25

Q.7

If a number x is 10% less than another number y and y is 10% more than 125, then x is equal to :

150

143

140.55

123.75

Ans .

123.75

Explanation :
y is 10% more than 125 = \(125 \times \frac{110}{100}\) = 137.5 = y

and x is 10% less than y

x = \(\frac{90}{100} \times y\)= \(\frac{90}{100} \times 137.5\) = 123.75

Q.8

Two numbers are respectively \(12 \frac{1}{2}\)% and 25% more than a third number. The first number as percentage of second number is

Ans .

Explanation :
If the third number is 100,then the numbers are

100 + \(\frac{25}{2}\) = \(\frac{225}{2}\) and 125 respectively.

∴ First number as a percentage of the second = \(\frac{225}{2 \times 125}\times 100\) = 90

Q.9

Which number is 40% less than 90 ?

Ans .

Explanation :
Required number = 60% of 90 = \(\frac{90 \times 60}{100}\) = 54

Q.10

Two numbers are less than a third number by 30% and 37% respectively. The per cent by which the second number is less than the first is

10%

Ans .

10%

Explanation :
Third number = 100

First number = 70

Second number = 63

∴ Required percentage = \(\frac{7}{70} \times 100\)= 10

Q.11

A number when reduced by 10% gives 30. The number is

\( 33 \frac{1}{2}\)

\( 33 \frac{1}{3}\)

Ans .

\( 33 \frac{1}{3}\)

Explanation :
Let the number be x then \(x \times \frac{90}{100}\) = 30

\(→\) x = \(\frac{3000}{90}\) = \(\frac{100}{3}\) = \( 33 \frac{1}{3}\)

Q.12

How much \( 66 \frac{2}{3}\)% of Rs. 312 exceeds Rs. 200?

Rs. 96

Rs. 4

Rs. 8

Rs. 104

Ans .

Rs. 8

Explanation :
According to the question,

Required difference

= Rs \(312 \times \frac{200}{3}%\) - 200

= Rs \(312 \times \frac{200}{300}\) - 200

= Rs. ( 208 - 200 ) = Rs. 8

Q.13

. A’s income is 25% more than B’s income. B’s income is what per cent of A’s income ?

Ans .

Explanation :
Let B’s income be Rs. 100.

∴ A’s income = Rs. 125

∴ Required per cent = \(\frac{100}{125} \times 100\) = 80%

Q.14

A’s salary is 50% more than that of B. Then B’s salary is less than that of A by

50%

\( 33 \frac{1}{3}\)%

\( 33 \frac{1}{4}\)%

\( 44 \frac{1}{2}\)%

Ans .

\( 33 \frac{1}{3}\)%

Explanation :
Required per cent = \(\frac{r}{100 + r} \times 100\)%

Required per cent = \(\frac{50}{100 + 50} \times 100\)

= \(\frac{100}{3}\) =\( 33 \frac{1}{4}\)%

Q.15

. If the salary of Manoj is 40% less than that of Subhash, then by how much percentage is the salary of Subhash more than that of Manoj?

60%

\( 66 \frac{1}{4}\)%

\( 66 \frac{2}{3}\)%

65%

Ans .

\( 66 \frac{2}{3}\)%

Explanation :
Required per cent = \(\frac{40}{100-40} \times 100\)

= \(\frac{40 \times 100}{60}\) = \( 66 \frac{2}{3}\)%

Q.16

. The percentage change in a number when it is first decreased by 10% and then increased by 10% is

0.1 % increase

1 % decrease

0.1 % decrease

No changes

Ans .

1 % decrease

Explanation :
Required per cent = \(\frac{-x^2}{100}\)%

= \(\frac{10 \times 10}{100}\) = –1%

Negative sign shows decrease

Q.17

x is 5 times longer than y. The percentage by which y is less than x is :

50%

40%

80%

70%

Ans .

80%

Explanation :
Length of Y = 1 foot

∴ Length of X = 5 feet

Required per cent = \(\frac{5-1}{5} \times 100\) = 80%

TYPE–III

Q.18

A person who spends \( 66 \frac{2}{3}\)% of his income is able to save 1,200 per month. His monthly expenses (in ₹) is :

1,200

2,400

3,000

3,200

Ans .

2,400

Explanation :
Savings = 100% - \( 66 \frac{2}{3}\)% = \( 33 \frac{1}{3}\)%

∵ \( 33 \frac{1}{3}\)% = ₹1200

∴ 100% = \( \frac{1200}{100} \times 3\times 100 \)% = ₹3600

∴ Expenses = 3600 – 1200 = ₹2400

Q.19

. The income of C is 20% more than B’s and the income of B is 25% more than A’s. Find by how much per cent is C’s income more than A’s ?

150%

50%

25%

35%

Ans .

50%

Explanation :
Suppose income of A = 100

∴ Income of B = 125

Income of C = 150

∴ Required percentage = \(\frac{50 \times 100}{100}\) = 50%

Q.20

If A’s income is 40% less than that of B, how much percent B’s income is more than that of A?

60%

40%

66.66%

33.33%

Ans .

66.66%

Explanation :
Required percentage

=\(\frac{x}{100-x} \times 100\)

=\(\frac{40}{60} \times 100\) = \(\frac{200}{3}\)= 66.66%

Q.21

. What per cent decrease in salaries would exactly cancel out the 20 per cent increase?

20%

\( 16 \frac{2}{3}\)%

\( 33 \frac{1}{3}\)%

18%

Ans .

\( 16 \frac{2}{3}\)%

Explanation :
Required answer = \(\frac{20}{100+20} \times 100\)% = \(\frac{20}{120} \times 100\)% = \(\frac{50}{3}\)% = \( 16 \frac{2}{3}\)%

Q.22

Income of A is 10% more than income of B. Let B’s income be x% less than A’s income. Find x.

\( 9 \frac{1}{11}\)%

\( 10 \frac{1}{11}\)%

11%

10%

Ans .

\( 9 \frac{1}{11}\)%

Explanation :
x = \(\frac{10}{10+100} \times 100\)% = \(\frac{1000}{110}\)% = \(\frac{100}{11}\)%= \(9\frac{1}{11}\)%

Q.23

If the income of Ram is \( 12 \frac{1}{2}\)% more than that of Shyam, the income of Shyam is less than that of Ram by

\( 11 \frac{1}{9}\)%

\( 13 \frac{1}{2}\)%

\( 87 \frac{1}{2}\)%

\( 88 \frac{1}{9}\)%

Ans .

\( 11 \frac{1}{9}\)%

Explanation :
Required %= \( \frac{R \times 100}{100+R}\)%

∴ Required % = \( \frac{12.5 \times 100}{100+12.5}\)% = \(\frac{1250}{112.5}\) = \(\frac{100}{9}\)= \( 11 \frac{1}{9}\)

Q.24

If 60% of A’s income is equal to 75% of B’s income, then B’s income is equal to x% of A’s income. The value of x is :

Ans .

Explanation :
Let A’s income = a

and B’s income = b

a × 60% = b × 75%

\(→\) a × 4 = 5 × b

\(→\) \(\frac{b}{a}\) = \(\frac{4}{5}\)

Now, b = a × x%

\(→\) \(\frac{b}{a}\) = \(\frac{x}{100}\)

\(→\) \(\frac{x}{100}\) = \(\frac{4}{5}\)

\(→\) x = \(\frac{4}{5} \times 100\) = 80

Q.25

A person gave 20% of his income to his elder son, 30% of the remaining to the younger son and 10% of the balance, he donated to a trust. He is left with 10080. His income was :

50000

40000

30000

20000

Ans .

20000

Explanation :

Let income be 100

∴ Sum given to elder son = 20% of 100 = 20

Remaining Sum = Rs. 80

Sum given to younger son = 30% of 80 = 24

Remaining sum = Rs. (80 – 24) = Rs. 56

Sum given to the trust = 10% of 56 = 5.6

∴ Remaining sum = (56 – 5.6) = 50.4

∴ When 50.4 remains, total income = 100

∴ When 10080 remains, total income = \(\frac{100 \times 10080}{50.4}\) = 20000

Q.26

Radha spends 40% of her salary on food, 20% on house rent, 10% on entertainment and 10% on conveyance. If her savings at the end of a month are 1500, then her salary per month (in ) is

8000

7500

6000

10000

Ans .

7500

Explanation :
Radha’s total percentage

expenditure = (40 + 20 + 10 + 10)% = 80%

Percentage savings =100 – 80 = 20%

Now, 20% of her total salary = 1500

Her total salary = \(\frac{1500 \times 100}{20}\) = 7500

Q.27

If the monthly salary of an employee is increased by \( 2 \frac{2}{3}\)% , he gets 72 rupees more. His monthly salary (in rupees) is

7200

3600

2700

2000

Ans .

2700

Explanation :
Suppose monthly income = x

Then, \(\frac{8}{3}\)% of x = 72

\(→\) \(x \times \frac{8}{300}\) = 72

\(→\) \(\frac{72 \times 300}{8}\) = 2700

Q.28

If the total monthly income of 16 persons is 80,800 and the income of one of them is 120% of the average income, then his income is

5,050

6,060

6,160

6,600

Ans .

6,060

Explanation :
Let the required income be x

Average monthly income = \(\frac{80800}{16}\) = 5050

∴ x = 120% of 5050

= \(\frac{120}{100} \times 5050\) = 6060

Q.29

Mita’s income is 25% more than that of Sita. What percent is Sita’s income less than that of Mita ?

25%

24%

\( 22 \frac{1}{2}\)%

20%

Ans .

20%

Explanation :
Required percentage =\(\frac{25}{100+25} \times 100\) = 20%

Q.30

A man spends \( 12 \frac{1}{2}\)% of his salary on items of daily use and 30% of the remainder on house rent. After that he is left with 2940. How much is his salary ?

4800

5200

4500

4000

Ans .

4800

Explanation :
Let man’s salary be x.

∴ His expenditure on items of daily use = \(\frac{25}{2}\)% of x

= \(\frac{25 \times x}{200}\) = \(\frac{x}{8}\)

So, remaining amount = x - \(\frac{x}{8}\) = \(\frac{7x}{8}\)

Expenditure on house rent = 30% of \(\frac{7x}{8}\)

= \(\frac{30}{100} \times \frac{7x}{8}\) = \(\frac{21x}{80}\)

Now, remaining amount = \(\frac{7x}{8} - \frac{21x}{80}\)

= \(\frac{70x - 21x}{80}\) = \(\frac{49x}{80}\)

According to the question,

∴ \(\frac{49x}{80}\) = 2940

x = \(\frac{2940 \times 80}{49}\) = 4800

Q.31

. The monthly income of a person was 13,500 and his monthly expenditure was 9,000. Next year his income increased by 14% and his expenditure increased by 7%. The per cent increase in his savings was

21%

28%

35%

Ans .

28%

Explanation :
Original savings

= (13500 – 9000)

= 4500

New income = 114% of 13500

= (114 × 135)

= 15390

New expenditure

= 107% of 9000

= (107 × 90)

= 9630

New savings

= (15390 – 9630)

= 5760

∴ Percentage increase in savings

= \(\frac{5760 - 4500}{4500} \times 100\)

= \(\frac{1260}{45}\) = 28%

Q.32

A worker suffers a 20% cut in his wages. He may regain his original wages by obtaining a rise of

27.5%

25.0%

22.5%

20.0%

Ans .

25.0%

Explanation :
Required percentage of increase

= \(\frac{r}{100 - r} \times 100\)

= \(\frac{20}{100 - 20} \times 100\)

= 25%

Q.33

. Given that 10% of A’s income = 15% of B’s income = 20% of C’s income. If sum of their income is 7800, then B’s income is:

3600

3000

2400

1800

Ans .

2400

Explanation :
10% of A = 15% of B = 20% of C

\(→\) 10A = 15B = 20C

\(→\)\(\frac{10A}{60}\) = \(\frac{15B}{60}\) = \(\frac{20C}{60}\)

\(→\)\(\frac{A}{6}\) = \(\frac{B}{4}\) = \(\frac{C}{3}\)

∴ A : B : C = 6 : 4 : 3

∴ 6x + 4x + 3x = 7800

\(→\) 13 x = 7800

\(→\) x = \(\frac{7800}{13}\) = 600

∴ B’s income = 4x

= 600 × 4 = 2400

Q.34

. If A’s income is 25% less than B’s income, by how much percent is B’s income more than that of A ?

25%

30%

\( 33 \frac{1}{3}\)%

\( 66 \frac{1}{3}\)%

Ans .

\( 33 \frac{1}{3}\)%

Explanation :
Required percentage = \(\frac{25}{100-25} \times 100\) = \(\frac{100}{3}\) =\( 33 \frac{1}{3}\)%

Q.35

A’s salary is 50% more than that of B. How much per cent is B’s salary less than that of A?

50%

\( 33 \frac{1}{3}\)%

45%

\( 66 \frac{2}{3}\)%

Ans .

\( 33 \frac{1}{3}\)%

Explanation :
Required percentage = \(\frac{50}{100+50} \times 100\)%

= \(\frac{50}{150} \times 100\)%

= \(\frac{100}{3}\)%

\( 33 \frac{1}{3}\)%

Q.36

Tulsiram’s salary is 20% more than that of Kashyap. If Tulsiram saves 720 which is 4% of his salary, then Kashyap’s salary is

15,000

12,000

10,000

22,000

Ans .

15,000

Explanation :
Let Tulsiram’s salary be x.

\(\frac{x \times 4}{100}\) = 720

x = \(\frac{720 \times 100}{4}\) = 18000

∴ Kashyap’s salary = \(\frac{100}{120} \times 18000\) = 15000

Q.37

. A’s salary is 40% of B’s salary and B’s salary is 25% of C’s salary. What percentage of C’s salary is A’s salary ?

10%

15%

20%

Ans .

10%

Explanation :
Let B’s salary = 100

∴ C’s salary = 400 and A’s salary = 40

∴ Required percentage = \(\frac{40}{400} \times 100\) = 10%

Q.38

If A’s income is 50% less than that of B’s, then B’s income is what per cent more than that of A ?

125%

100%

75%

50%

Ans .

100%

Explanation :
Required percentage = \(\frac{50}{100-50} \times 100\)

Otherwise \(→\) Let's B income = 100 \(→\) A income = 50.

Required % = \(\frac{100 - 50}{50} \times 100\) = 100%

Q.39

X’s income is 20% more than that of Y. What per cent is Y’s income less than X ?

\( 83 \frac{1}{3}\)%

\( 16 \frac{2}{3}\)%

\( 83 \frac{2}{3}\)%

\( 16 \frac{1}{3}\)%

Ans .

\( 16 \frac{2}{3}\)%

Explanation :
∴ Required percentage

= \(\frac{20}{100+20} \times 100\)

= \(\frac{50}{3}\) = \( 16 \frac{2}{3}\)%

Q.40

The allowances of an empolyee constitutes 165% of his basic pay. If he receives 11925 as gross salary, then his basic pay is (in ) :

4000

5000

4500

5500

Ans .

4500

Explanation :
Basic pay of the employee = 11925 × \(\frac{100}{265}\) = 4500

Q.41

If Nita’s salary is 25 per cent more than Papiya’s salary, then the percentage by which Papiya’s salary is less than Nita’s salary is

15%

20%

25%

32%

Ans .

20%

Explanation :
Required percentage = \(\frac{25}{100+25} \times 100\) = \(\frac{25}{125} \times 100\)

= 20%

Q.42

The salary of a person is decreased by 25% and then the decreased salary is increased by 25%. His new salary in comparison with his original salary is

the same

6.25% more

6.25% less

0.625% less

Ans .

6.25% less

Explanation :
Effective change = (–25 + 25 –\(\frac{25 \times 25}{100}\))%

= –6.25%

The negative sign shows decrease.

Q.43

Ram saves 14% of his salary while Shyam saves 22%. If both get the same salary and Shyam saves 1540, what is the savings of Ram?

990

980

890

880

Ans .

980

Explanation :
If Shyam’s salary be x, then

\(\frac{22 \times x}{100}\) = 1540

x = \(\frac{1540 \times 100}{22}\) = 7000

∴ Ram’s savings = \(\frac{14 \times 7000}{100}\) = 980

Q.44

A's salary is 25% more than B's salary. B's salary is how much less than A's salary ?

20 %

24 %

25 %

27.5 %

Ans .

20 %

Explanation :
Required percentage =\(\frac{25}{125} \times 100\) = 20%

Q.45

A man spends 75% of his income. His income increased by 20% and he increased his expenditure by 15%. His savings will then be increased by

33%

\( 33 \frac{1}{3}\)%

35%

40%

Ans .

35%

Explanation :
Let man’s income = 100

Savings = 100 – 75 = 25

New income = 120

Savings = 120 - \(\frac{75 \times 115}{100}\) = 120 - \(\frac{345}{4}\)

= \(\frac{480 - 345}{4}\) = \(\frac{135}{4}\)

Increase in savings

= \(\frac{135}{4}\) - 25 = \(\frac{35}{4}\)

∴ Percentage increase

\(\frac{\frac{35}{4}}{25} \times 100\) = 35%

Q.46

Nitin’s salary was reduced by 10% and then the reduced salary was increased by 10%. His new salary in comparison with his original salary is

the same

1% more

1% less

5% less

Ans .

1% less

Explanation :
Let Nitin’s initial salary be 100

After 10% reduction,

New salary = 90% of 100 = 90

Again after 10% increase

New salary = \(\frac{90 \times 110}{100}\) = 99

∴ Percentage decrease =1 %

Q.47

A man spends 40% of his monthly salary on food and one-third of the remaining on transport. If he saves 4,500 per month, which is equal to half the balance after spending on food and transport, his monthly salary is

11,250

22,500

25,000

45,000

Ans .

22,500

Explanation :
Suppose monthly income of the man is Rs. x.

Expenditure on food = 40% of x = \(\frac{2x}{5}\)

Remaining amount = x –\(\frac{2x}{5}\) = \(\frac{3x}{5}\)

Expenditure on transport = \(\frac{1}{3} \times \frac{3x}{5}\) = \(\frac{x}{5}\)

Remaining amount = \(\frac{3x}{5} - \frac{x}{5}\) = \(\frac{2x}{5}\)

\(\frac{1}{2} \times \frac{2x}{5}\) = 4500

∴ x = 4500 × 5 = 22,500

Q.48

A saves 20% of his monthly salary. If his monthly expenditure is 6,000, then his monthly savings is

1,500

1,800

1,200

4,800

Ans .

1,500

Explanation :
If the monthly income of A is

x, then \(\frac{x \times 80}{100}\) = 6000

x = \(\frac{6000 \times 100}{80}\) = 7500

∴ Savings = 7500 – 6000

= 1500

Q.49

A’s salary is increased by 10% and then decreased by 10%. Then, change in salary is

1% decrease

1% increase

2% decrease

Ans .

1% decrease

Explanation :
Change in salary

= -\(\frac{10 \times 10}{100}\)= –1%

Negative sign shows decrease.

Q.50

Kishan spends 30% of his salary on food and donates 3% in a Charitable Trust. He spends 2,310 on these two items, then total salary for that month is

6,000

8,000

9,000

7,000

Ans .

7,000

Explanation :
If the total salary of Kishan be

x, then \(x \times \frac{33}{100}\) = 2310

x = \(\frac{2310 \times 100}{33}\) = 7000

Q.51

A clerk received an annual salary of 3,660 in the year 1975. This was 20% more than his salary in 1974. What was his salary in 1974 ?

3,005

3,000

3,500

3,050

Ans .

3,050

Explanation :
Salary of clerk in 1974 = \(\frac{3660 \times 100}{100+20}\) = 3050

Q.52

Out of his total income, Mr. Kapur spends 20% on house rent and 70% of the rest on house-hold expenses. If he saves 1,800, what is his total income (in rupees)?

7,800

7,000

8,000

7,500

Ans .

7,500

Explanation :
Total percentage of expenditure = 20 + \(\frac{80 \times 70}{100}\)% = 76%

If total income be x, then

\(x \times \frac{24}{100}\) = 1800

x = \(\frac{1800 \times 100}{24}\) = 7500

Q.53

Out of his total income, Mr. Kapur spends 20% on house rent and 70% of the rest on house-hold expenses. If he saves 1,800, what is his total income (in rupees)?

7,800

7,000

8,000

7,500

Ans .

7,500

Explanation :
Total percentage of expenditure

=\((20 + \frac{80 \times 70}{100})%\) = 76%

If total income be x, then

\(x \times \frac{24}{100}\) = 1800

x = \(\frac{1800 \times 100}{24}\) = 7,500

Q.54

Arbind spends 75% of his income and saves the rest. His income is increasesd by 20% and he increases his expenditure by 10%. Then the increase in savings in percentage is

55%

52%

50%

48%

Ans .

50%

Explanation :
Arbind’s income = 100

Expenditure = 75

Savings = 25

New income = 120

Expenditure = 75 + 7.5 = 82.5

Savings = 120 – 82.5 = 37.5

Required percentage

= \(\frac{37.5-25}{25} \times 100\) = 50%

Q.55

The enhanced salary of a man becomes 24,000 after 20% increment. His previous salary was

20,000

21,000

16,000

18,000

Ans .

20,000

Explanation :
Man’s previous salary = \(24000 \times \frac{100}{120}\) = 20,000

Q.56

The salary of a person was reduced by 10%. By what per cent should his reduced salary be raised so as to bring it at par with his original salary ?

\( 11 \frac{1}{9}\)%

\( 9 \frac{1}{11}\)%

11%

Ans .

\( 11 \frac{1}{9}\)%

Explanation :
Required per cent increase

= \(\frac{r}{100-r} \times 100\)%

= \(\frac{10}{100-10} \times 100\) = \(\frac{100}{9}\)

\( 11 \frac{1}{9}\)%

Q.57

. If A’s salary is 50% more than that of B, then B’s salary is less than A’s by

33%

\( 40 \frac{1}{3}\)%

\( 45 \frac{1}{3}\)%

\( 33 \frac{1}{3}\)%

Ans .

\( 33 \frac{1}{3}\)%

Explanation :
Required percentage = \(\frac{R}{100 + R } \times 100\)

= \(\frac{50}{100 + 50 } \times 100\)

= \(\frac{50}{150 } \times 100\)

= \(\frac{100}{3}\)

\( 33 \frac{1}{3}\)%

Q.58

Mr. X spends 35% of his salary on food and 5% of his salary on children education. In January 2011, he spent 17, 600 on these two items. His salary for that month is

40, 000

44, 000

48, 000

46, 000

Ans .

44, 000

Explanation :
Pecentage of expenditure on food and education = 35 + 5 = 40%

If the monthly salary of X be Rs. x, then \(\frac{x \times 40}{100}\) = 17600

\(→\) x × 40 = 17600 × 100

\(→\) x =\(\frac{1760000}{40}\) = 44000

Q.59

The monthly salaries of A and B together amount to Rs. 40,000. A spends 85% of his salary and B, 95% of his salary. If now their savings are the same, then the salary (in Rs.) of A is

Rs. 10,000

Rs. 12,000

Rs. 16,000

Rs. 18,000

Ans .

Rs. 10,000

Explanation :
A’s monthly salary = Rs. x

∴ B’s monthly salary

= Rs. (40000 – x)

A spends 85% of his income.

∴ A’s savings = \(\frac{15x}{100}\) = rs. \(\frac{3x}{20}\)

B’s savings = (40000 – x) × \(\frac{5}{100}\)

= rs. \(\frac{40000 - x}{20}\)

∴ \(\frac{3x}{20}\) = \(\frac{40000 - x}{20}\)

\(→\) 3x = 40000 – x

\(→\) 4x = 40000

\(→\) x = \(\frac{40000}{4}\)= Rs. 10000

Q.60

25% of annual salary of A is equal to eighty percent of annual salary of B. Monthly salary of B is 40% of the monthly salary of C. Annual salary of C is Rs. 6 lac. What is the monthly salary of A ?

Rs. 60,000

Rs. 62,000

Rs. 64,000

Rs. 56,000

Ans .

Rs. 64,000

Explanation :
C’s monthly salary

= \(\frac{600000}{12}\)= Rs. 50000

B’s monthly salary = \(\frac{50000 \times 40}{100}\)

= Rs. 20000

\(\frac{1}{4}\) of A’s monthly salary

= \(\frac{20000 \times 80}{100}\)

\(→\) A’s monthly salary

= Rs. (16000 × 4)

= Rs. 64000

Q.61

Two numbers are less than a third number by 30% and 37% respectively. How much percent is the second number less than the first ?

Ans .

Explanation :
Let the third number be 100.

∴ First number = 70

Second number = 63

Required percent = \(\frac{70 - 63}{70} \times 100\)

= \(\frac{7}{70} \times 100\) = 10%

Q.62

. A man spends 75% of his income. His income is increased by 20% and he increased his expenditure by 10%. His savings are increased by

\( 37 \frac{1}{2}\)%

50%

25%

10%

Ans .

50%

Explanation :
Man’s income = Rs. 100 (let).

∴ Expenditure = Rs. 75

Savings = Rs. 25

New income = Rs. 120

Expenditure = \(\frac{75 \times 110}{100}\) = Rs. 82.5

Savings = Rs. (120 – 82.5) = Rs. 37.5

∴ Required percentage = \(\frac{37.25 - 25}{25} \times 100\)

= \(\frac{12.5 \times 100}{25}\) = 50%

Q.63

Ram babu donated 3% of his income to a charity and deposited 12% of the rest in bank. If now he has Rs. 12804, then his income was :

Rs. 17460

Rs. 15000

Rs. 7500

Rs. 14550

Ans .

Rs. 15000

Explanation :
Let Ram Babu’s salary be Rs. x.

Remaining amount after donations to charity

= Rs \(\frac{97x}{100}\)

After depositing money in the bank, Remaining amount

= \(\frac{97x}{100} \times \frac{88}{100}\)

\(\frac{97x \times 88}{10000}\) = 12804

\(→\) x = \(\frac{12804 \times 10000}{97 \times 88}\) = Rs. 15000

Q.64

. Mukesh has twice as much money as Soham. Soham has 50% more money than Pankaj. If the average money with them is Rs.110, then Mukesh has

Rs. 155

Rs. 160

Rs. 180

Rs. 175

Ans .

180

Explanation :
Amount with Soham = Rs. x (let).

∴ Amount with Mukesh = Rs. 2x

Amount with Pankaj = \(\frac{100x}{150}\) = Rs. \(\frac{2x}{3}\)

∴ Soham : Mukesh : Pankaj = x

:2x:\(\frac{2x}{3}\) = 3 : 6 : 2

Sum of the terms of ratio

= 3 + 6 + 2 = 11

∴ Amount with Mukesh

= Rs \(\frac{6}{11} \times 300\)

= Rs. 180

Q.65

. A man spends 75% of his income. His income increases by 20% and his expenditure also increases by 10%. Find the percentage increase in his savings.

25%

50%

15%

10%

Ans .

50%

Explanation :
Let man’s income be Rs. 100.

∴ Expenditure = Rs. 75

Savings = Rs. 25

Case–II,

Man’s income = Rs. 120

Expenditure = \(\frac{75 \times 110}{100}\)

= Rs. 82.5

Savings = 120 – 82.5 = Rs. 37.5

∴ Percentage increase

= \(\frac{37.5-25}{25} \times 100\)

= \(\frac{12.5}{25} \times 100\) = 50%

Q.66

Christy donated 10% of his income to an orphanage and deposited 20% of the remainder in his bank. If he has now Rs. 7200 left, what is his income.

Rs. 10000

Rs. 8000

Rs. 9000

Rs. 8500

Ans .

Rs. 10000

Explanation :
Christy’s income = Rs. x (let)

Amount given to orphanage = Rs. \(\frac{x}{10}\)

Remaining amount = Rs \(\frac{9x}{10}\)

Remaining amount after depositing in bank

= 80% of \(\frac{9x}{10}\)

= Rs. \(\frac{9x}{10} \times \frac{80}{100}\)

= Rs. \(\frac{18x}{25}\)

According to the question,

\(\frac{18x}{25}\) = 72000

\(→\) 18x = 25 × 7200

\(→\) x = \(\frac{25 \times 7200}{18}\) = Rs. 10000

Q.67

The average salary of male employees in a firm was Rs. 5200 and that of females was Rs. 4200. The mean salary of all the employees was Rs. 5000. What is the percentage of female employees?

80%

20%

40%

30%

Ans .

20%

Explanation :
Let the number of male employees in the firm be x and that

of female employees be y. According to the question,

\(\frac{5200 \times x + 4200 \times y }{x + y}\) = 5000

\(→\) 52x + 42y = 50 (x + y)

\(→\) 52x + 42y = 50x + 50y

\(→\) 52x – 50x = 50y – 42y

\(→\) 2x = 8y

\(→\) x = 4y

∴ x + y = 4y + y = 5y

∴ Required percent = \(\frac{y}{5y} \times 100\) = 20%

Q.68

In a factory, the salary of each worker is increased in the ratio 22 : 25 but the number of workers is decreased by \( 26 \frac{2}{3}\)% The net effect on the salary is

\( 11 \frac{1}{9}\)% decrease

20% increase

\( 16 \frac{2}{3}\)% decrease

10% increase

Ans .

#####

Explanation :
22 : 25 = \(\frac{22}{25} \times 100\) = 88%

∴ Percentage effect

= 88 - \(\frac{80}{3}\) - \(\frac{88 \times 80}{300}\) %

= 88 - \(\frac{80}{3}\) - \(\frac{704}{30}\) %

= \(\frac{2640 - 800 - 704}{30}\) %

= \(\frac{1136}{30}\) = 37.86% increase

Q.69

If the income of Mohan is 150% higher than that of Mahesh, then by what percent the income of Mahesh is less than that of Mohan ?

40%

50%

60%

45%

Ans .

60%

Explanation :
Mahesh’s income = Rs. 100 (let).

∴ Mohan’s income = Rs. 250

Required per cent = \(\frac{250 -100}{250} \times 100\)%

= \(\frac{1500}{25}\)% = 60%

Q.70

A man spends 60% of his income on different items. His income is increased by 20% and his expenditure is also increased by 10%. Find the percentage decrease in his savings?

10%

15%

20%

25%

Ans .

10%

Explanation :
Let person’s income be Rs. 100.

Expenses = Rs. 60

Savings = Rs. 40

New income = Rs. 120

Expenses = Rs \(\frac{120 \times 70}{100}\) = Rs. 84

Savings = Rs. (120 – 84) = Rs. 36

∴ Required percent decrease = \(\frac{40 - 36}{40} \times 100\) = \(\frac{400}{40}\) = 10%

Q.71

P’s salary is 25% higher than Q, what percentage is Q’s salary lower than that of P ?

\( 33 \frac{1}{3}\)

Ans .

Explanation :
Q,s salary = Rs. 100 (let).

∴ P’s salary = 125

∴ Required per cent = \(\frac{125 - 100}{125} \times 100\)

= \(\frac{25 \times 100}{125}\) = 20%

Q.72

. If A’s salary is 40% less than that of B, then how much percent is B’s salary more than that of A?

\( 33 \frac{1}{3}\)%

\( 66 \frac{2}{3}\)%

\( 33 \frac{2}{3}\)%

\( 66 \frac{1}{3}\)%

Ans .

\( 66 \frac{2}{3}\)%

Explanation :
Required per cent

= \(\frac{40}{100-40} \times 100\)

= \(\frac{4000}{60}\)

= \(\frac{200}{3}\) = \( 66 \frac{2}{3}\)%

Q.73

. A’s salary was decreased by 50% and subsequently increased by 50%. How much per cent does he lose?

25%

50%

\( 12 \frac{1}{2}\)%

No loss

Ans .

25%

Explanation :
Effect on percentage = \(\frac{-x^2}{100}\)%

= \(\frac{-50 \times 50}{100}\)%

= –25%

Negative sign shows decrease.

Q.74

A man spends 15% of his income. If his expenditure is Rs. 75, his income (in rupees) is :

400

300

750

500

Ans .

500

Explanation :
Let the man’s income be Rs. x.

According to the question,

\(x \times \frac{15}{100}\) = 75

\(→\) x = \(\frac{75 \times 100}{15}\) = Rs. 500

Q.75

. If A’s salary is 30% more than that of B, then by how much percent is B’s salary less than that of A ?

13.01%

13.07%

23.07%

23.01%

Ans .

23.07%

Explanation :
B’s salary = Rs. 100 (let)

∴ A's salary = Rs. 130

∴ Required percent = \(\frac{30}{130} \times 100\) = \(\frac{300}{13}\) = 23 07%

Q.76

. The average monthly salary of all the employees in a factory is Rs. 8840. If the average salary of all the officers is Rs. 15000 and that of the remaining employees is Rs. 8000, then what is the percentage of the officers among the employees?

10%

12%

\( 8 \frac{1}{3}\)%

11%

Ans .

12%

Explanation :
Number of officers = x.

Number of remaining employees = y.

According to the question,

8840 (x + y) = 15000x + 8000y

\(→\) 8840x + 8840y

= 15000x + 8000y

\(→\) 15000x – 8840x

= 8840y – 8000y

\(→\) 6160x = 840y

\(\frac{x}{y}\) = \(\frac{840}{6160}\) = \(\frac{3}{22}\)

∴ Required per cent = \(\frac{3}{25} \times 100\) = 12%

Q.77

The monthly salary of Mr. Sachdev gets increased by 5%, thereby his salary becomes 15,120 per annum. His earlier monthly salary (before the increase) was

1,320

1,200

1,240

1,440

Ans .

1,200

Explanation :
Let annual salary of Sachdev before increase be Rs. x.

According to the question,

\(x \times \frac{105}{100}\) = 15120

\(→\) x = \(\frac{15120 \times 100}{105}\)

= Rs. 14400

∴ Required monthly salary

= \(\frac{14400}{12}\) = Rs. 1200

TYPE–IV

Q.78

If A exceeds B by 40%, B is less than C by 20%, then A : C is :

28 : 25

26 : 25

3 : 2

3 : 1

Ans .

28 : 25

Explanation :
Let B = 100

∴ According to question,

A is 40% greater than B.

∴ A = 140

∴ B is 20% less than C

∴ 0.8C = 100

∴ C = 125

∴ A : C = 140 : 125 = 28 : 25

Q.79

If 10% of m is the same as 20% of n, then m : n is equal to :

2 : 1

1 : 2

1 : 10

1 : 20

Ans .

2 : 1

Explanation :
10% of m = 20% of n

∴ \(\frac{10}{100} \times m\) = \(\frac{20}{100} \times n\)

∴ \(\frac{m}{n}\) = \(\frac{10}{5}\) = \(\frac{2}{1}\)

∴ m : n = 2 : 1

Q.80

The ratio 5 : 4 expressed as a per cent equals :

125%

80%

40%

12.5%

Ans .

125%

Explanation :
5 : 4 when expressed as percent = \(\frac{5}{4} \times 100\) = 125%

Q.81

The ratio of the number of boys and girls in a college is 3 : 2. If 20% of boys and 25% of girls are adults, the percentage of those students who are not adults, is

58%

67.5%

78%

82.5%

Ans .

78%

Explanation :
Let the number of boys and girls in the college be 3x and 2x respectively.

Number of minor boys = \(3x \times \frac{80}{100}\) = \(\frac{12x}{5}\)

Number of minor girls = \(2x \times \frac{75}{100}\) = \(\frac{3x}{2}\)

Total number of minor students = \(\frac{12x}{5}\) + \(\frac{3x}{2}\)

= \(\frac{24x + 15x}{10}\) =\(\frac{39x}{10}\)

Required percentage = \(\frac{39x}{10 \times 5x} \times 100\) = 78%

Q.82

The ratio of the number of boys to that of girls in a school is 4 : 1. If 75% of boys and 70% of the girls are scholarship-holders, then the percentage of students who do not get scholarship is

50%

28%

75%

26%

Ans .

26%

Explanation :
Let the number of boys and

girls be 4x and x respectively.

Number of boys who hold scholarship. = \(\frac{75}{100} \times 4x\) = 3x

Number of girls who hold scholarship = \(\frac{70 \times x}{100}\) = \(\frac{7x}{10}\)

Number of students who do not hold scholarship

= 5x - 3x - \(\frac{7x}{10}\) = 2x - \(\frac{7x}{10}\)= \(\frac{13x}{10}\)

The required percentage = \(\frac{\frac{13x}{10}}{5x} \times 100\)

= \(\frac{13x}{10 \times 5x} \times 100\) = 26%

Q.83

Two numbers are in the ratio 2 : 3. If 20% of the smaller number added to 20 is equal to the sum of 10% of the larger number and 25, then the smaller number is

100

160

180

200

Ans .

100

Explanation :
Let the numbers be 2x and 3x.

According to the question,

\(\frac{20}{100} \times 2x\) + 20 = \(\frac{10}{100} \times 3x\) + 25

\(\frac{2x}{5}\) + 20 = \(\frac{3x}{10}\) + 25

\(→\) x = 50

∴ The smaller number = 2x = 100

Q.84

Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is

2 : 5

3 : 5

4 : 5

6 : 7

Ans .

4 : 5

Explanation :
Let the third number be 100.

∴ First number = 120

Second number = 150

∴ Required ratio = \(\frac{120}{150}\) = \(\frac{4}{5}\)

Q.85

The difference of two numbers is 45% of their sum. The ratio of the larger number to the smaller number is

20 : 9

9 : 20

11 : 29

29 : 11

Ans .

29 : 11

Explanation :
Let the numbers be x and y

and x is greater than y. Then

x – y = 45% of (x + y)

\(→\) x – y =\(\frac{45}{100}\)(x + y)

\(→\) x – y =\(\frac{9}{20}\)(x + y)

\(→\) 20x – 20y = 9x + 9y

\(→\) 20x – 9x = 20y + 9y

\(→\) 11x = 29y

∴ 29 : 11

Q.86

If 30% of A = 0.25 of B =\(\frac{1}{5}\) of C, then A : B : C is equal to :

5 : 6 : 4

5 : 24 : 5

6 : 5 : 4

10 : 12 : 15

Ans .

10 : 12 : 15

Explanation :
30% of A = 25% of B

\(→\) 30 A = 25 B

\(→\) A : B = 25 : 30 = 5 : 6

Again, 25% of B = 20% of C

\(→\) 25 B = 20C

\(→\) 5B = 4C

\(→\) B : C = 4 : 5

∴ A : B : C = 5 × 4 : 4 × 6 : 6 × 5

= 20 : 24 : 30 = 10 : 12 : 15

Q.87

In a class, the number of girls is 20% more than that of the boys. The strength of the class is 66. If 4 more girls are admitted to the class, the ratio of the number of boys to that of the girls is

1 : 2

3 : 4

1 : 4

3 : 5

Ans .

3 : 4

Explanation :
Let number of boys be x.

Then \( x + \frac{120}{100}x = 66\)

\(→\) \(\frac{5x + 6x}{5}\) = 66

\(→\) x = \(\frac{66 \times 5}{11}\) = 30

∴ Number of girls

= 66 – 30 = 36

∴ New ratio = 30 : (36 + 4)

= 30 : 40 = 3 : 4

Q.88

The ratio of the number of boys and girls in a school is 3 : 2. If 20% of the boys and 30% of the girls are scholarship holders, then the percentage of students, who do not get scholarship, is

50%

72%

75%

76%

Ans .

76%

Explanation :
Let the number of boys = 3x and that of girls = 2x

Number of boys who do not hold scholarship = 80% of 3x = \(3x \times \frac{80}{100}\) = \(\frac{12x}{5}\)

Number of girls who do not hold scholarship = \(2x \times \frac{70}{100}\) = \(\frac{14x}{10}\)

∴ Number of students who do not hold scholarship = \(\frac{12x}{5}\) + \(\frac{14x}{10}\)

= \(\frac{24x + 14x}{10}\) = \(\frac{38x}{10}\)

∴ Required percentage = \(\frac{\frac{38x}{10}}{5x} \times 100\)

= \(\frac{38}{10 \times 5} \times 100\) = 76%

Q.89

. The expenses on rice, fish and oil of a family are in the ratio 12 : 17 : 3. The prices of these articles are increased by 20%, 30% and 50% respectively. The total expenses of family on these articles are increased by

\( 14 \frac{1}{8}\)%

\( 7 \frac{1}{8}\)%

\( 56 \frac{1}{8}\)%

\( 28 \frac{1}{8}\)%

Ans .

\( 28 \frac{1}{8}\)%

Explanation :
Let the initial expenses on rice, fish and oil be 12x, 17x and 3x respectively.

∴ Total expenditure

= (12x + 17x + 3x)

= 32 x

After increase, Expenditure on rice = \(\frac{120}{100} \times 12x\) = 14.4x

Expenditure on fish = \(\frac{130}{100} \times 17x\) = 22.1x

Expenditure on oil = \(\frac{150}{100} \times 3x\) = 4.5x

Total expenditure

= (14.4 x + 22.1x + 4.5 x)

= 41 x

Increase = (41x – 32x)

= 9x

∴ Percentage increase

= \(\frac{9x}{32x} \times 100\) = \(\frac{225}{8}\) = \( 28 \frac{1}{8}\)%

Q.90

If 20% of A = 30% of B =\(\frac{1}{6}\) of C, then A : B : C is

2 : 3 : 16

3 : 2 : 16

10 : 15 : 18

15 : 10 : 18

Ans .

15 : 10 : 18

Explanation :
20 % of A = 30 % of B = \(\frac{1}{6}\) of C

\(→\) \(\frac{20A}{100}\) = \(\frac{30B}{100}\) = \(\frac{C}{6}\)

\(→\) \(\frac{A}{5}\) = \(\frac{B}{\frac{10}{3}}\) = \(\frac{C}{6}\) = k (let)

\(→\) A = 5k, B = \(\frac{10}{3}\)k C = 6 k

∴ A : B : C = 5k :\(\frac{10}{3}\)k:6 k

= 15 : 10 : 18

Q.91

The bus fare and train fare of a place from Kolkata were 20 and 30 respectively. Train fare has been increased by 20% and the bus fare has been increased by 10%. The ratio of new train fare to new bus fare is

11 : 18

18 : 11

5 : 3

3 : 5

Ans .

18 : 11

Explanation :
Increased train fare = \(\frac{120}{100} \times 30\) = 36

Increased bus fare = \(\frac{110}{100} \times 20\) = 22

∴ Required ratio = 36 : 22

= 18 : 11

Q.92

. The difference of two numbers is 15% of their sum. The ratio of the larger number to the smaller number is

23 : 17

11 : 9

17 : 11

23 : 11

Ans .

23 : 17

Explanation :
Let the numbers be x and y where x > y. Then,

x - y = \(\frac{15}{100}\) (x + y)

\(→\) x - y = \(\frac{3}{20}\) (x + y)

\(→\) 20x – 20y = 3x + 3y

\(→\) 20x – 3x = 20y + 3y

\(→\) 17x = 23y \(→\) \(\frac{x}{y}\) = \(\frac{23}{17}\)

Q.93

The price of sugar is increased by 20%. If the expenditure on sugar has to be kept the same as earlier, the ratio between the reduction in consumption and the original consumption is

1 : 3

1 : 4

1 : 6

1 : 5

Ans .

1 : 6

Explanation :
The raised price = \(\frac{120}{100}\) of the former price

∴ The householder must now consume \(\frac{100}{120}\) of the original amount

∴ The reduction in consumption = 1 - \(\frac{100}{120}\) of the original consumption

= \(\frac{1}{6}\) of the original consumption

i.e. 1 : 6

Q.94

. Rama’s expenditures and savings are in the ratio 5 : 3. If her income increases by 12% and expenditure by 15%, then by how much per cent do her savings increase ?

12%

13%

Ans .

Explanation :
Let Rama’s expenditure = 5x

Savings = 3x

∴ Rama’s income = 5x + 3x = 8x

After increase,

Rama’s income = \(\frac{112}{100} \times 8x\) = 8.96 x

Rama’s expenditure = \(\frac{5x \times 115}{100}\) = 5.75x

Rama’s savings

= (8.96x – 5.75x)

= 3.21x

∴ Rama’s saving per cent = \(\frac{3.21x - 3x}{3x} \times 100\)

= \(\frac{0.21}{3x} \times 100\) = 7

Q.95

. The ratio of two numbers is 4:5 when the first is increased by 20% and the second is decreased by 20%, the ratio of the resulting numbers is

4 : 5

5 : 4

5 : 6

6 : 5

Ans .

6 : 5

Explanation :
Let the numbers be 4x and

5x . After corresponding

increase or decrease,

Required ratio

= \(4x \times \frac{120}{100}\) : \(5x \times \frac{80}{100}\)

= 12x : 10x

= 6 : 5

Q.96

If 60% of A = \(\frac{3}{4}\) of B, then A : B is

9 : 20

20 : 9

4 : 5

5 : 4

Ans .

5 : 4

Explanation :
\(\frac{A \times 60}{100}\) = \(B \times \frac{3}{4}\)

\(A \times \frac{ 3}{5}\) = \(B \times \frac{3}{4}\)

A : B = 5 : 4

Q.97

If A exceeds B by 60% and B is less than C by 20%, then A : C is

32 : 25

25 : 32

8 : 5

4 : 5

Ans .

32 : 25

Explanation :
Let C = 100

∴ B = 80

A = \(\frac{80 \times 160}{100}\) = 128

∴ A : C = 128 : 100 = 32 : 25

Q.98

If 30% of (B – A) = 18% of (B + A), then the ratio A : B is equal to

4 : 1

1 : 4

5 : 4

5 : 9

Ans .

1 : 4

Explanation :
\((B - A) \times \frac{30}{100}\) = \((B + A) \times \frac{18}{100}\)

\(\frac{B - A}{B + A}\) = \(\frac{18}{30}\) = \(\frac{3}{5}\)

By componendo and dividendo,

\(\frac{2B}{-2A}\) = \(\frac{3+5}{3-5}\) = \(\frac{8}{-2}\) = \(\frac{4}{-1}\)

\(→\) A : B = 1 : 4

Q.99

The ratio of the number of boys and girls in a school is 3 : 2. If 20% of the boys and 25% of the girls are scholarship holders, then the percentage of the students, who do not get the scholarship, is :

78%

75%

60%

55%

Ans .

78%

Explanation :
Boys = 30, Girls = 20 (let)

Boys getting no scholarship = 24

Girls getting no scholarship = 15

Sum = 24 + 15 = 39

∴ Required percentage = \(\frac{38}{50} \times 100\) = 78%

Q.100

When 60% of a number is subtracted from another number, the second number reduces to its 52%; the ratio of the first number to the second number is :

6: 5

5: 3

5: 4

4: 5

Ans .

4: 5

Explanation :
Let the first number be x and

second number be y.

∴ y - \(\frac{60x}{100}\) = \(\frac{52y}{100}\)

\(→\) 100y – 60x = 52y

\(→\) 48y = 60x

∴ \(\frac{x}{y}\) = \(\frac{48}{60}\) = \(\frac{4}{5}\) or 4 : 5

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