- Staff Selection Commission Mathematics - Percentage (1999-2017)

Staff Selection Commission Mathematics - Percentage (1999-2017)

TYPE–II

Ans .

33$$\frac{1}{3}$$%

1. Explanation :

Let y be 100.

∴ x = 75

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

Ans .

9$$\frac{1}{11}$$%

1. Explanation :

Required per cent decrease = $$\frac{10}{100+10} \times 100$$ = $$\frac{10}{110} \times 100$$ = 9$$\frac{1}{11}$$%

Ans .

9$$\frac{1}{11}$$%

1. 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$$\frac{1}{11}$$%

Ans .

25%

1. Explanation :

Required percentage = $$\frac{20}{100-20} \times\ 100$$ = 25%

Ans .

20%

1. Explanation :

Required percentage = $$\frac{25}{100 +25} \times 100$$ = 20%

Ans .

25

1. 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

Ans .

123.75

1. 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

Ans .

90

1. 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

Ans .

54

1. Explanation :

Required number = 60% of 90 = $$\frac{90 \times 60}{100}$$ = 54

Ans .

10%

1. Explanation :

Third number = 100

First number = 70

Second number = 63

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

Ans .

$$33 \frac{1}{3}$$

1. Explanation :

Let the number be x then $$x \times \frac{90}{100}$$ = 30

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

Ans .

Rs. 8

1. 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

Ans .

80

1. Explanation :

Let B’s income be Rs. 100.

∴ A’s income = Rs. 125

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

Ans .

$$33 \frac{1}{3}$$%

1. Explanation :

Required per cent = $$\frac{r}{100 + r} \times 100$$%

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

= $$\frac{100}{3}$$ =$$33 \frac{1}{4}$$%

Ans .

$$66 \frac{2}{3}$$%

1. Explanation :

Required per cent = $$\frac{40}{100-40} \times 100$$

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

Ans .

1 % decrease

1. Explanation :

Required per cent = $$\frac{-x^2}{100}$$%

= $$\frac{10 \times 10}{100}$$ = –1%

Negative sign shows decrease

Ans .

80%

1. Explanation :

Length of Y = 1 foot

∴ Length of X = 5 feet

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

TYPE–III

Ans .

2,400

1. 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

Ans .

50%

1. Explanation :

Suppose income of A = 100

∴ Income of B = 125

Income of C = 150

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

Ans .

66.66%

1. Explanation :

Required percentage

=$$\frac{x}{100-x} \times 100$$

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

Ans .

$$16 \frac{2}{3}$$%

1. Explanation :

Required answer = $$\frac{20}{100+20} \times 100$$% = $$\frac{20}{120} \times 100$$% = $$\frac{50}{3}$$% = $$16 \frac{2}{3}$$%

Ans .

$$9 \frac{1}{11}$$%

1. Explanation :

x = $$\frac{10}{10+100} \times 100$$% = $$\frac{1000}{110}$$% = $$\frac{100}{11}$$%= $$9\frac{1}{11}$$%

Ans .

$$11 \frac{1}{9}$$%

1. Explanation :

Required %= $$\frac{R \times 100}{100+R}$$%

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

Ans .

80

1. 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

Ans .

20000

1. 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

Ans .

7500

1. Explanation :

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

Ans .

2700

1. Explanation :

Suppose monthly income = x

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

$$→$$ $$x \times \frac{8}{300}$$ = 72

$$→$$ $$\frac{72 \times 300}{8}$$ = 2700

Ans .

6,060

1. Explanation :

Let the required income be x

Average monthly income = $$\frac{80800}{16}$$ = 5050

∴ x = 120% of 5050

= $$\frac{120}{100} \times 5050$$ = 6060

Ans .

20%

1. Explanation :

Required percentage =$$\frac{25}{100+25} \times 100$$ = 20%

Ans .

4800

1. 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

Ans .

28%

1. 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%

Ans .

25.0%

1. Explanation :

Required percentage of increase

= $$\frac{r}{100 - r} \times 100$$

= $$\frac{20}{100 - 20} \times 100$$

= 25%

Ans .

2400

1. 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

Ans .

$$33 \frac{1}{3}$$%

1. Explanation :

Required percentage = $$\frac{25}{100-25} \times 100$$ = $$\frac{100}{3}$$ =$$33 \frac{1}{3}$$%

Ans .

$$33 \frac{1}{3}$$%

1. Explanation :

Required percentage = $$\frac{50}{100+50} \times 100$$%

= $$\frac{50}{150} \times 100$$%

= $$\frac{100}{3}$$%

$$33 \frac{1}{3}$$%

Ans .

15,000

1. 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

Ans .

10%

1. Explanation :

Let B’s salary = 100

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

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

Ans .

100%

1. 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%

Ans .

$$16 \frac{2}{3}$$%

1. Explanation :

∴ Required percentage

= $$\frac{20}{100+20} \times 100$$

= $$\frac{50}{3}$$ = $$16 \frac{2}{3}$$%

Ans .

4500

1. Explanation :

Basic pay of the employee = 11925 × $$\frac{100}{265}$$ = 4500

Ans .

20%

1. Explanation :

Required percentage = $$\frac{25}{100+25} \times 100$$ = $$\frac{25}{125} \times 100$$

= 20%

Ans .

6.25% less

1. Explanation :

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

= –6.25%

The negative sign shows decrease.

Ans .

980

1. 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

Ans .

20 %

1. Explanation :

Required percentage =$$\frac{25}{125} \times 100$$ = 20%

Ans .

35%

1. 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%

Ans .

1% less

1. 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 %

Ans .

22,500

1. 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

Ans .

1,500

1. 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

Ans .

1% decrease

1. Explanation :

Change in salary

= -$$\frac{10 \times 10}{100}$$= –1%

Negative sign shows decrease.

Ans .

7,000

1. Explanation :

If the total salary of Kishan be

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

x = $$\frac{2310 \times 100}{33}$$ = 7000

Ans .

3,050

1. Explanation :

Salary of clerk in 1974 = $$\frac{3660 \times 100}{100+20}$$ = 3050

Ans .

7,500

1. 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

Ans .

7,500

1. 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

Ans .

50%

1. 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%

Ans .

20,000

1. Explanation :

Man’s previous salary = $$24000 \times \frac{100}{120}$$ = 20,000

Ans .

$$11 \frac{1}{9}$$%

1. Explanation :

Required per cent increase

= $$\frac{r}{100-r} \times 100$$%

= $$\frac{10}{100-10} \times 100$$ = $$\frac{100}{9}$$

$$11 \frac{1}{9}$$%

Ans .

$$33 \frac{1}{3}$$%

1. Explanation :

Required percentage = $$\frac{R}{100 + R } \times 100$$

= $$\frac{50}{100 + 50 } \times 100$$

= $$\frac{50}{150 } \times 100$$

= $$\frac{100}{3}$$

$$33 \frac{1}{3}$$%

Ans .

44, 000

1. 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

Ans .

Rs. 10,000

1. 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

Ans .

Rs. 64,000

1. 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

Ans .

10

1. 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%

Ans .

50%

1. 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%

Ans .

Rs. 15000

1. 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

Ans .

180

1. 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

Ans .

50%

1. 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%

Ans .

Rs. 10000

1. 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

Ans .

20%

1. 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%

Ans .

#####

1. 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

Ans .

60%

1. 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%

Ans .

10%

1. 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%

Ans .

20

1. 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%

Ans .

$$66 \frac{2}{3}$$%

1. Explanation :

Required per cent

= $$\frac{40}{100-40} \times 100$$

= $$\frac{4000}{60}$$

= $$\frac{200}{3}$$ = $$66 \frac{2}{3}$$%

Ans .

25%

1. Explanation :

Effect on percentage = $$\frac{-x^2}{100}$$%

= $$\frac{-50 \times 50}{100}$$%

= –25%

Negative sign shows decrease.

Ans .

500

1. 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

Ans .

23.07%

1. Explanation :

B’s salary = Rs. 100 (let)

∴ A's salary = Rs. 130

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

Ans .

12%

1. 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%

Ans .

1,200

1. 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

Ans .

28 : 25

1. 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

Ans .

2 : 1

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

Ans .

125%

1. Explanation :

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

Ans .

78%

1. 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%

Ans .

26%

1. 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%

Ans .

100

1. 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

Ans .

4 : 5

1. Explanation :

Let the third number be 100.

∴ First number = 120

Second number = 150

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

Ans .

29 : 11

1. 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

Ans .

10 : 12 : 15

1. 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

Ans .

3 : 4

1. 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

Ans .

76%

1. 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%

Ans .

$$28 \frac{1}{8}$$%

1. 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

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

Ans .

15 : 10 : 18

1. 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

Ans .

18 : 11

1. 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

Ans .

23 : 17

1. 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 $$→$$ $$\frac{x}{y}$$ = $$\frac{23}{17}$$

Ans .

1 : 6

1. 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

Ans .

7%

1. 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

Ans .

6 : 5

1. 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

Ans .

5 : 4

1. 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

Ans .

32 : 25

1. Explanation :

Let C = 100

∴ B = 80

A = $$\frac{80 \times 160}{100}$$ = 128

∴ A : C = 128 : 100 = 32 : 25

Ans .

1 : 4

1. 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

Ans .

78%

1. 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%

Ans .

4: 5

1. 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