- 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 = $$\frac{\frac{1}{10}}{\frac{11}{20}} \times 100$$ = $$\frac{200}{11}$$%