- Staff Selection Commission Mathematics - Percentage

Staff Selection Commission Mathematics - Percentage (1999-2017)


TYPE–I





Ans .

160


  1. Explanation :

    \(A \times\frac{80}{100} = B \times\frac{50}{100}\)

    \( ∴ B = \frac{A\times80}{100}= 1.6A\)

    \( ∴ B = 160% of A\)

    \( ∴ x = 160\)







Ans .

125% of x


  1. Explanation :

    \( y = \frac{100 \times 100}{80}\) of x

    ∴ y = 125% of x







Ans .

10% of y


  1. Explanation :

    \(\frac{8x}{100}=\frac{4y}{100}\)

    ∴y = 2x

    ∴20% of x = 10% of y







Ans .

64%


  1. Explanation :

    Let x be the multiplicand.

    ∴Error = \(\frac{5}{3} x - \frac{3}{5}x\)

    \(=\frac{25x-9x}{15}=\frac{16x}{15}\)

    ∴Percentage error

    = \(\frac{\frac{16x}{15}}{\frac{5}{3}x}\times100\)

    =\(\frac{16x}{15}\times\frac{3}{5x}\times100=64%\)







Ans .

60


  1. Explanation :

    p% of p = 36

    ∴\(\frac{p}{100}\times p=36\)

    ∴\(p^2=3600\)

    ∴p = 60







Ans .

4


  1. Explanation :

    Let 2 be x% of 50

    x% of 50 = 2

    \(\frac{x}{100}\times50=2\)

    \(\frac{x}{2}=2\)

    ∴ x = 4







Ans .

200%


  1. Explanation :

    Let x % of \(\frac{1}{3}\) = \(\frac{2}{3}\)

    x% = \(\frac{2\times3}{3}\) = 2

    x = 200%







Ans .

₹5


  1. Explanation :

    0.15% of 33\(\frac{1}{3}%\) of ₹ 10000

  2. =\(\frac{0.15}{100}\times\frac{100}{300}\times10000\) = ₹5






Ans .

240


  1. Explanation :

    30% of x = 72

    ∴ x = \(\frac{72\times100}{30}=240\)







Ans .

400%


  1. Explanation :

    15% of (A + B)

    = 25% of (A – B)

    =>\(\frac{15}{100}\)(A+B) = \(\frac{25}{100}\)(A-B)

    => 15 (A + B) = 25 (A – B)

    => 15 A + 15 B = 25A – 25 B

    => 10 A = 40 B

    => A = 4 B

    Now, let x% of B is equal to A

    ∴\(\frac{x}{100}\times B\) = A =>\(\frac{x}{100}\times B\) = 4B

    ∴ x = 400%







Ans .

15


  1. Explanation :

    20% of 25% of 300

    =\(\frac{20}{100}\times \frac{25}{100} \times 300\)

    =\(\frac{1}{5}\times \frac{1}{4} \times 300\) = 15







Ans .

1200


  1. Explanation :

    x% of \(\frac{25}{2}\) = 150

    =>\(\frac{x}{100} \times \frac{25}{2}\) = 150

    =>\(\frac{x}{8}\) = 150

    => x = 150 × 8 = 1200







Ans .

25%


  1. Explanation :

    50% of (x – y)

    = 30% of (x + y)

    =>\(\frac{1}{2}\)(x-y)=\(\frac{3}{10}\)(x+y)

    =>\(\frac{x}{2}\) - \(\frac{3x}{10}\)=\(\frac{3y}{10}\) + \(\frac{y}{2}\)

    =>\(\frac{5x-3x}{10}\)=\(\frac{3y+5y}{10}\)

    =>\(\frac{x}{5}\)=\(\frac{4y}{5}\)

    ∴ x = 4y

    =>y =\(\frac{x}{4}\) or \(\frac{x}{4}\times 100\) % = 25x







Ans .

50


  1. Explanation :

    P\(\times \frac{50}{100} \) = Q\(\times \frac{25}{100} \)

    => P × 50 = Q × 25

    => P = \(\frac{Q \times 25}{50}\) => P = \(\frac{Q}{2}\)

    P = Q x %

    ∴ \(\frac{Q \times x}{100}\) = \(\frac{Q}{2}\)

    => x = \(\frac{100}{2}\) = 50







Ans .

40%


  1. Explanation :

    20% of A = 50% of B

    2A = 5B => A = \(\frac{5B}{2}\)

    Let B is x % of A.

    \(\frac{5B}{2} \times \frac{x}{100} = B\)

    => x = \frac{200}{5} = 40%







Ans .

8%


  1. Explanation :

    Since 18% of the students neither play football nor cricket. It means 82% of the students either play football or cricket or both.

    Using set theory

    ∴n(A\({\displaystyle \cup }\)B) = n(A)+n(B)-n(A\({\displaystyle \cap }\)B)

    => 82 = 40 + 50 - n(A\({\displaystyle \cap }\)B)

    ∴n(A\({\displaystyle \cap }\)B) = 90 – 82 = 8

    ∴ 8% students play both games.







Ans .

7 : 3


  1. Explanation :

    \(\frac{20(P+Q)}{100}\) = \(\frac{50}{100}(P-Q)\)

    \(\frac{P+Q}{P-Q}\) = \(\frac{5}{2}\)

    \(\frac{2P}{2Q}\) = \(\frac{5+2}{5-2}_{\;\;\;\;\;\;\ By \; componendo \; and \; dividendo}\)

    \(\frac{P}{Q}\) = \(\frac{7}{3}\) or 7 : 3







Ans .

10


  1. Explanation :

    Let x % × 0.1 = 0.01

    \(\frac{x}{100}\times 0.1\) = 0.01

    x = \(\frac{0.01 \times 100}{0.1}\) = 10







Ans .

\(\frac{13}{4}\)


  1. Explanation :

    Required percentage

    = \(\frac{65}{2000}\times 100\) = \(\frac{13}{4}\)

    [∵ 2kg = 2000g]







Ans .

0.005


  1. Explanation :

    1% = \(\frac{1}{100}\)

    ∴ \(\frac{1}{100}\times \frac{1}{2}\) = \(\frac{1}{200}\) = 0.005







Ans .

7.292 %


  1. Explanation :

    1 hour 45 minutes

    = 1\(\frac{3}{4} hours = \frac{7}{4} hours\)

    1 day = 24 hours

    ∴ Required per cent

    = \(\frac{\frac{7}{4}}{24} \times 100\)

    = \(\frac{7}{4 \times 24} \times 100\)

    = 7.292%







Ans .

60%


  1. Explanation :

    Required percentage = \(\frac{1.14}{1.91} \times 100 = 60%\)







Ans .

40%


  1. Explanation :

    Required percentage = \(\frac{32}{40} \times 100 = 40%\)







Ans .

300


  1. Explanation :

    \(A \times \frac{90}{100} = \frac{B \times 30}{100}\)

    \(→\) A × 3 = B

    \(→\) A × x% = A × 3

    \(→\) \(\frac{x}{100} = 3 → x = 300 \)







Ans .

400


  1. Explanation :

    \(\frac{A \times 90}{100} = \frac{B \times 30}{100}\)

    \(→\) 3A = B

    \(→\) \(3A = \frac{A \times 2x}{100}\)

    \(→\) 300 = 2x \(→\) x = 150







Ans .

75%


  1. Explanation :

    \(A \times \frac{30}{100} + \frac{B \times 40}{100} = \frac{B \times 80}{100}\)

    \(→\) A × 30 = B × 40

    \(→\) \(\frac{A}{B} = \frac{40}{30} = \frac{4}{3}\)

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

    \(→\) \(\frac{B}{A} \times 100 = \frac{3}{4} \times 100 = 75%\)







Ans .

\(\frac{7}{6}\)


  1. Explanation :

    \((A+B) \times \frac{40}{100}\)

    \((A-B) \times \frac{60}{100}\)

    \(→\) 2 (A + B) = 3 (A – B)

    \(→\) 2A + 2B = 3A – 3B

    \(→\) A = 5B

    ∴\(\frac{2A-3B}{A+B} = \frac{10B-3B}{5B+B}\)

    = \(\frac{7B}{6B} = \frac{7}{6}\)







Ans .

0.1%


  1. Explanation :

    \( 0.1% = \frac{0.1}{100} = 0.001 \)







Ans .

2%


  1. Explanation :

    Required percentage = \( \frac{70}{3.5 \times 1000} \times 100 = 2\% \)







Ans .

300%


  1. Explanation :

    \(\frac{1}{3}\) of 1206 = 1206 \(\times \frac{1}{3} \) = 402

    ∴ Required percent

    = \(\frac{402}{134} \times 100 = 300\% \)







Ans .

5


  1. Explanation :

    \(a \times \frac{120}{100} = b \times \frac{80}{100} \)

    \(→\) \(\frac{b}{a}\) = \( \frac{120}{80} \) = \( \frac{3}{2} \)

    ∴ \(\frac{b+a}{b-a}\) = \(\frac{\frac{b}{a}+1}{\frac{b}{a}-1}\) = \(\frac{\frac{3}{2}+1}{\frac{3}{2}-1}\) = \(\frac{\frac{5}{2}}{\frac{1}{2}}\) = 5







Ans .

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


  1. Explanation :

    (A + B) \(\times \frac{20}{100}\) = B \(\times \frac{50}{100}\)

    \(\frac{A + B}{5}\) = \(\frac{B}{2}\)

    \(2A + 2B = 5B\)

    \(2A = 3B\)

    \(\frac{2A}{B}\) = 3 or 2A = 3B

    ∴ \(\frac{2A - B}{2A + B}\) = \(\frac{2\frac{A}{B} - 1}{2\frac{A}{B} + 1}\) = \(\frac{3 - 1}{3 + 1}\)

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







Ans .

\(\frac{zx}{y}\)% of a


  1. Explanation :

    \(\frac{ax}{100}\) = \(\frac{by}{100}\)

    \(→\) b = \(\frac{ax}{y}\)

    ∴ z% of b = \(\frac{ax}{y}\times \frac{z}{100}\)

    = \(\frac{xz}{y}\)% of a







Ans .

2


  1. Explanation :

    60 × 60 × \(\frac{y}{100}\)

    = 1 minute 12 seconds

    \(→\) 36y = 72 \(→\) y = 2







Ans .

2%


  1. Explanation :

    Required percentage = \(\frac{72}{3.6\times 1000} \times 100 = 2%\)







Ans .

30,000


  1. Explanation :

    Let the total number of employees be x.

    ∴ x \(\times \frac{402}{134}\) = 20700

    ∴ x = \(\frac{20700 \times 100}{69}\) = 30000







Ans .

60%


  1. Explanation :

    Required percentage = \(\frac{24}{40} \times 100\) = 60%







Ans .

80


  1. Explanation :

    \(x \times \frac{125}{100}\) = 100

    \(x = \frac{100 \times 100}{125}\) = 80







Ans .

600


  1. Explanation :

    \(x \times \frac{83}{100}\) = 498

    \(x = \frac{498 \times 100}{83}\) = 600







Ans .

20%


  1. Explanation :

    Let C = 100

    Then, A = 150

    B = 125

    ∴ Required percentage

    = \(\frac{150-125}{125} \times 100\) = 20%







Ans .

50000


  1. Explanation :

    If the number of trees in the garden be x, then

    \(x \times \frac{60}{100} \times \frac{25}{100} \times \frac{20}{100}\) = 1500

    \(→\)\(x \times \frac{3}{5} \times \frac{1}{4} \times \frac{1}{5}\) = 1500

    \(→\)x = \(\frac{1500 \times 5 \times 4 \times 5}{3}\)

    = 50000







Ans .

88%


  1. Explanation :

    Males = 25000 \(\times \frac{4}{5}\) = 20000

    Females = 5000

    Educated males = \( \frac{20000 \times 95}{100}\) = 19000

    Educated Females = \( \frac{5000 \times 60}{100}\) = 3000

    Total educated persons = 22000

    ∴ Required per cent = \( \frac{22000}{25000} \times 100\) = 88%







Ans .

36


  1. Explanation :

    Required number = \(\frac{240 \times 25}{100} - \frac{160 \times 15}{100}\)

    = 60 – 24 = 36







Ans .

135


  1. Explanation :

    First part = ₹x and second part = ₹y

    ∴ \(\frac{x \times 80}{100}\) = \(\frac{y \times 60}{100}\) + 3

    \(\frac{4x}{5}\) = \(\frac{3y}{5}\) + 3

    4x – 3y = 15 ...(i)

    Again,

    \(\frac{4}{5}\) = \(\frac{9x}{10}\) + 3

    8y = 9x + 60

    8y – 9x = 60 ...(ii)

    By equation (i) × 8 + (ii) × 3,

    32x – 24y = 120

    24y – 27x = 180
    \(\frac{\hspace{80pt}}{\:}\)
    5x = 300 \(→\) x = 60

    From equation (i)

    4 × 60– 3y = 15

    \(→\) 3y = 240 – 15 = 225

    \(→\) y = \(\frac{225}{3}\) = 75

    ∴ x + y = 60 + 75 = 135







Ans .

80


  1. Explanation :

    Group A = 40%

    Group B = \(\frac{60 \times 75}{100}\) = 45%

    Group C = 15%

    If the total number of students be x, then

    \( \frac{x\times 15}{100} \)= 12

    x = \( \frac{12\times 100}{15} \) = 80







Ans .

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


  1. Explanation :

    After taking away respective balls,

    Number of balls in the box= 75 + 25 + 50 = 150

    ∴ Percentage of black balls = \( \frac{50}{150} \times 100\) = \( \frac{100}{30}\) = 33\(\frac{1}{3}\)%







Ans .

4 pairs


  1. Explanation :

    ∵ S.P. of a dozen pairs of socks

    = \(\frac{180 \times 80}{100}\) = ₹144

    S.P. of 1 pair of socks

    ∴ S.P. of 1 pair of socks = \(\frac{144}{12}\) = ₹12

    No of pairs available for ₹48 = \(\frac{48}{12}\)= 4







Ans .

100


  1. Explanation :

    Let the number be x

    \(\frac{3}{5} \times \frac{60}{100} \times x\) = 36

    x = \(\frac{36 \times 5\times 5}{3\times 3}\) = 100







Ans .

25


  1. Explanation :

    \(\frac{P-Q}{2}\) = \((P+Q) \times \frac{30}{100}\)

    \(→\) 5(P – Q) = (P + Q) × 3

    \(→\) 5P – 3P = 5Q + 3Q

    \(→\) 2P = 8Q

    \(→\) P = 4Q = \(4 \times \frac{P \times x}{100})\







Ans .

90


  1. Explanation :

    Let greater number be x.

    ∴ Smaller number = 150 – x

    According to the question,

    \(\frac{40 \times x}{100}\) = \(\frac{60 \times (150-x)}{100}\)

    \(→\) 2x = 3 × 150 – 3x

    \(→\) 5x = 3 × 150

    \(→\) x = 90







Ans .

400


  1. Explanation :

    Let the number be x. According to the question

    80% of x + 80 = x

    \(→\)\(\frac{80x}{100}\) + 80 = x

    \(→\)\(\frac{4x}{5}\) + 80 = x

    \(→\)\(\frac{x}{5}\) = 80 \(→\) x = 400







Ans .

720


  1. Explanation :

    Suppose number be x 20% of x = 120

    \(x \times \frac{20}{100}\) = 120

    \(x = \frac{120 \times 100}{20}\) = 600

    600 \(\times\) 120% = 600 \(\times\) \(\frac{120}{100}\) = 720







Ans .

150


  1. Explanation :

    Let the number be x. Then x – 60% of x = 60

    \(→\) x – 0.60x= 60

    \(→\) 0.4x = 60

    \(→\) x = \(\frac{60}{0.4}\)

    \(→\) x = \(\frac{600}{4}\)

    x = 150

    ∴ The number is 150







Ans .

300


  1. Explanation :

    Let number be x.

    ∴ According to question,

    75% of x + 75 = x

    \(\frac{3x}{4}\) + 75 = x

    x - \(\frac{3x}{4}\) = 75

    x = 75 × 4 = 300







Ans .

40%


  1. Explanation :

    Let the third number be x,

    According to the question;

    First number = \(\frac{20}{100} \times x\) = \(\frac{x}{5}\)

    Second number = \(\frac{50}{100} \times x\) = \(\frac{x}{2}\)

    ∴ Required percentage

    = \(\frac{\frac{x}{5} \times 100}{\frac{x}{3}}\) = \(\frac{x}{5} \times \frac{2}{x} \times 100\) = 40%







Ans .

93.75%


  1. Explanation :

    Rule : If two numbers are respectively x% and y% less than the third number, first number as a percentage of second is

    \(\frac{100-x}{100-y} \times 100%\)

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

    = \(\frac{75}{80} \times 100%\) = 93 75%







Ans .

60


  1. Explanation :

    According to question

    x + \(\frac{x \times 150}{100}\) = 150

    \(→\) x + \(\frac{x \times 3}{2}\) = 150

    \(→\) 2x + 3x = 2 × 150 = 300

    \(→\) 5x = 300 \(→\) x = 60







Ans .

50


  1. Explanation :

    Let the number be x.

    According to the question,

    \(x \times \frac{18}{100}\) = \(75 \times \frac{12}{100}\)

    \(→\)x = \(\frac{75 \times 12}{18}\) = 50







Ans .

5395


  1. Explanation :

    Let the numbers be x and y and x > y.

    According to the question,

    \(6\frac{1}{2}%\) of x = \(8\frac{1}{2}%\) of y

    or \(\frac{13}{2}%\) of x = \(\frac{17}{2}%\) of y

    or 13x = 17y

    or x = \(\frac{17}{13}y\)

    ∴ \(\frac{17}{13}y - y = 1660\)

    or \(\frac{17y - 13y}{13} = 1660\)

    or 4y = 1660 × 13

    y = \(\frac{1660 \times 13}{4} = 5395\)







Ans .

120


  1. Explanation :

    If the number be x, then

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

    \(→\)\(\frac{3x}{4}\) + 75 = x

    \(→\)x - \(\frac{3x}{4}\) = 75

    \(→\) \(\frac{x}{4}\) = 75

    \(→\) x = 4 × 75 = 300

    ∴ 40% of 300

    = \(\frac{300 \times 40}{100}\) = 120







Ans .

37


  1. Explanation :

    Number to be added = x (let)

    ∴ \(\frac{320 \times 10}{100}\) + x = \(\frac{230 \times 30}{100}\)

    \(→\) 32 + x = 69

    \(→\) x = 69 – 32 = 37







Ans .

\(\frac{1}{5}\), -4


  1. Explanation :

    X is 20% less than Y.

    If Y = 100, X = 80

    \(\frac{Y-X}{Y}\) = \(\frac{100 - 80}{100}\)

    = \(\frac{20}{100}\) = \(\frac{1}{5}\)

    \(\frac{X}{X-Y}\) = \(\frac{80}{80-100}\)

    = \(\frac{80}{-20}\) = -4







Ans .

0.025


  1. Explanation :

    1% of 1% of 25% of 1000

    \( = 1000 \times \frac{25}{100} \times \frac{1}{100} \times \frac{1}{100}\)

    = 0.025







Ans .

\(\frac{2}{7}\)


  1. Explanation :

    \(\frac{120 \times 25}{100}\) + \(\frac{380 \times 40}{100}\)

    = 637 × ?

    \(→\) 30 + 152 = 637 × ?

    \(→\) 182 = 637 × ?

    \(→\) ? = \(\frac{182}{637}\) = \(\frac{2}{7}\)







Ans .

4620


  1. Explanation :

    Population of the illiterate in the village

    = (100 – 30)% of 6600

    = \(\frac{6600 \times 70}{100}\) = 4620







Ans .

10% of y


  1. Explanation :

    8% of x = 4% of y

    \(→\) \(\frac{x \times 8}{100}\) = \(\frac{y \times 4}{100}\)

    \(→\) x = \(\frac{4 \times y}{8}\) = \(\frac{y}{2}\)

    ∴ 20% of x = \(\frac{20}{100}\) of \(\frac{y}{2}\)

    = \(\frac{10}{100}\) of y

    = 10% of y







Ans .

2


  1. Explanation :

    Let the number be x.

    ∴ \(x \times \frac{3}{4} \times \frac{4}{5} \times \frac{40}{100}\) = 48

    \(→\) \(x \frac{3}{5} \times \frac{2}{5}\) = 48

    \(→\) \(x = \frac{48 \times 5 \times 5}{3 \times 2}\) = 200

    ∴ 1% of 200

    = \(200 \times \frac{1}{100} = 2\)







Ans .

4.114


  1. Explanation :

    Required sum

    = \(\frac{24.2 \times 16}{100}\) + \(\frac{2.42 \times 10}{100}\)

    = 3.872 + 0.242

    = 4.114







Ans .

\(\frac{1}{30}\)%


  1. Explanation :

    x% of 15 hours = 18 seconds

    \(→\) x% of 15 × 60 × 60 seconds

    = 18 seconds

    \(→\) \(\frac{15 \times 60 \times 60 \times x}{100}\) = 18

    \(→\) x = \(\frac{18}{15 \times 6 \times 6 }\)% = \(\frac{1}{30}\)%







Ans .

28125


  1. Explanation :

    \(80 \times \frac{y}{100}\times \frac{x}{100}\)

    = \(\frac{900 \times 25}{100}\)

    \(→\) \(\frac{xy \times 80}{10000} = 9 \times 25\)

    \(→\) xy = \(\frac{9 \times 25 \times 10000}{80}\) = 28125







Ans .

25 days


  1. Explanation :

    Required time = \(\frac{35 \times 100}{140}\) = 25 days







Ans .

500


  1. Explanation :

    According to the question,

    \(\frac{60A}{100}\) = \(\frac{30B}{100}\)

    \(→\) \(\frac{3A}{5}\) = \(\frac{3B}{10}\) = \(\frac{3}{10} \times \frac{40C}{100}\)

    \(→\) \(\frac{3A}{5}\) = \(\frac{3C}{25}\) = \(\frac{3A}{25} \times \frac{x}{100}\)

    \(→\) \(\frac{3}{5}\) = \(\frac{3x}{2500}\)

    \(→\) 5x = 2500

    \(→\) x = \(\frac{2500}{5}\) = 500







Ans .

42


  1. Explanation :

    Total staff strength in the office = 100 (let)

    Females = 40

    Males = 60

    Married females = \(\frac{40 \times 70}{100}\) = 28

    Unmarried females = 40 – 28 = 12

    Unmarried males = 30

    ∴ Unmarried staff

    = 30 + 12 = 42

    i.e. 42%







Ans .

100


  1. Explanation :

    Let the number be x.

    According to the question,

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

    \(→\)\(\frac{x}{2} + 50\) = x

    \(→\)\(x - \frac{x}{2}\) = 50

    \(→\)\(\frac{x}{2}\) = 50

    \(→\) x = 100







Ans .

125


  1. Explanation :

    Let the required amount be Rs. x.

    According to the question,

    \(90 \times 83\frac{1}{3}% = x \times 60%\)

    \(→\)\(90 \times \frac{250}{3}% = x \times 60%\)

    \(→\) x = \(\frac{30 \times 250}{60}\) = ₹ 125







Ans .

350


  1. Explanation :

    Let the whole number be x.

    According to the question,

    51% of x = 714

    \(\frac{x \times 51}{100}\) = 714

    x = \(\frac{714 \times 100}{51}\) = 1400

    ∴ 25% of 1400

    = \(\frac{1400 \times 25}{100}\) = 350







Ans .

Rs. 27


  1. Explanation :

    Initial price of eggs = Rs. x per dozen (let).

    New price = Rs \(\frac{3x}{4}\)per dozen

    According to the question,

    \(\frac{162}{\frac{3x}{4}}\) - \(\frac{162}{x}\) = 2

    \(→\)\(\frac{216}{x}\) - \(\frac{162}{x}\) = 2

    \(→\)\(\frac{54}{x}\) = 2

    \(→\) 2x = 54

    \(→\) x = Rs. 27 per dozen







Ans .

2.083


  1. Explanation :

    Required percent = \(\frac{30}{24 \times 60} \times 100\) = 2.083







Ans .

75%


  1. Explanation :

    Initial number of mangoes = 300

    Number of remaining mangoes = 300 – 75 = 225

    Required percent = \(\frac{225}{300} \times 100\) = 75%







Ans .

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


  1. Explanation :

    Required percent = \(\frac{3.5}{7.5}\times 100\)

    = \(\frac{3500}{75}\) = \(\frac{140}{3}\)

    = 46\(\frac{2}{3}\)%







Ans .

20%


  1. Explanation :

    Discount percent = \(\frac{1}{5} \times 100 = 20%\)







Ans .

20%


  1. Explanation :

    B’s income = Rs. 100

    ∴ A’s income = Rs. 125

    ∴ Required percent

    = \(\frac{125-100}{125} \times 100\)

    = \(\frac{2500}{125}\) = 20%







Ans .

2.5%


  1. Explanation :

    1 day = 24 hours = (24 × 60) minutes

    ∴ Required percent = \(\frac{36}{24 \times 60} \times 100\) = 2.5%







Ans .

16


  1. Explanation :

    Let the larger number be x.

    ∴ Smaller number = \(\frac{25x}{100}\) = \(\frac{x}{4}\)

    According to the question,

    \(x-\frac{x}{4} = 12\)

    \(→\) \(\frac{3x}{4}\) = 12

    \(→\) 3x = 12 × 4

    x = \(\frac{12 \times 4}{3}\) = 16







Ans .

55


  1. Explanation :

    Initial number of students in the class = x

    According to the question,

    \(x \times \frac{120}{100}\) = 66

    \(→\) x = \(\frac{66 \times 100}{120}\) = 55







Ans .

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


  1. Explanation :

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

    = \(\frac{2000}{140}\)= \(\frac{50}{3}\) = 16\(\frac{2}{3}\)%







Ans .

10000


  1. Explanation :

    Number of goats before flood = x (let)

    According to the question,

    \(x \times \frac{88}{100}\times \frac{95}{100}\) = 8360

    \(→\) x =\(\frac{8360 \times 100 \times 100}{88 \times 95}\) = 10000







Ans .

5


  1. Explanation :

    Let, C = 100

    ∴ B = \(100 \times \frac{25}{100}\) = 25

    ∴ A = \( \frac{20}{100} \times 25\) = 5

    ∴ x % of C = 5

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

    \(→\) x = 5







Ans .

Rs. 720900


  1. Explanation :

    Number of boys in the school = \(\frac{1500 \times 56}{100}\) = 840

    Number of girls = (1500 – 840) = 660

    Monthly fee of each boy = Rs. 540

    Monthly fee of each girl = Rs \(\frac{540 \times 75}{100}\) = Rs. 405

    ∴ Total monthly fee of boys and girls

    = Rs. (840 × 540 + 660 × 405)

    = Rs. (453600 + 267300)

    = Rs. 720900







Ans .

756


  1. Explanation :

    Percentage of children = (100 – 54 – 32)%

    = 14%

    According to the question,

    ∵ 14% = 196

    ∵ 1% = \(\frac{196}{14}\) = 14

    ∴ 54% = 54 × 14 = 756 men







Ans .

200


  1. Explanation :

    Expression = \(\frac{25}{4}\)% of 1600 + \(\frac{25}{2}\)% of 800

    = \(\frac{1600 \times 25}{400}\) + \(\frac{800 \times 25}{200}\)

    = 100 + 100 = 200







Ans .

25


  1. Explanation :

    Required percent = \(\frac{25}{100} \times 100\) = 25%







Ans .

50


  1. Explanation :

    Required percent = \(\frac{40}{80} \times 100\) = 50%







Ans .

\(\frac{200}{11}\)%


  1. Explanation :

    Correct answer = 1 – \((\frac{1}{4}+\frac{1}{5})\)

    = 1 – \(\frac{9}{20}\) = \(\frac{11}{20}\)

    Incorrect answer = 0.45 = \(\frac{45}{100}\) = \(\frac{9}{20}\)

    Error = \(\frac{11}{20}\) - \(\frac{9}{20}\)= \(\frac{1}{10}\)

    Percentage error = \(\frac{\frac{1}{10}}{\frac{11}{20}} \times 100\) = \(\frac{200}{11}\)%