- 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 :

    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







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