Exercise 2

1. A = 10% of x, B = 10% of y, C = 10% of x + 10% of y. On the basis of the above equalities, what is true in the following?
(a) A is equal to B
(b) A is greater than B
(c) B is greater than A
(d) Relation cannot be established between A and B
(e) None of these

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Ans.d

The given information gives no indication regarding the comparison of x and y.

2. If inflation increases at a rate of 8 p.c.p.a. what will a 20 article cost at the end of two years?
(a) Between 20 and 21
(b) Between 21 and 22
(c) Between 22 and 23
(d) Between 23 and 24
(e) None of these

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Ans.d

Required sum

= $20\left(1 + \frac{8}{100} \right)^{2} = \frac{20 \times 27 \times 27}{25 \times 25} = 23.3$

3. In a recent survey 40% houses contained two or more people. Of those houses containing only one person 25% were having only a male. What is the percentage of all houses which contain exactly one female and no males?
(a) 75
(b) 40
(c) 15
(d) Cannot be determined
(e) None of these

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Ans.e

Houses containing only one person = 100 – 40 = 60%

Houses containing only a male = 60 × 25100 = 15%

∴ Houses containing only one female = 60 – 15 = 45%

4. Sumitra has an average of 56% on her first 7 examinations. How much should she make on her eighth examination to obtain an average of 60% on 8 examinations?
(a) 88%
(b) 78%
(c) 98%
(d) Cannot be determined
(e) None of these

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Ans.d

Since the weight age of eighth examination is not known, hence can not be determined.

5. If 3x + 7 = x2 + M = 7x + 5, what is the value of 120% of M?
(a) 8.90
(b) 9.90
(c) 9.98
(d) Cannot be determined
(e) None of these

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Ans.b

If 3x + 7 = x2 + M = 7x + 5

ie, 3x + 7 = 7x + 5

or, 4x = 2 ∴ x = 12

and 3x + 7 = x2 + M

or, 14 + M = 32 + 7 ⇒ M + 14 = 8 + 12

∴ M = 814

6. Four-fifths of three-eighths of a number is 24. What is 250 per cent of that number?
(a) 100
(b) 160
(c) 120
(d) 200
(e) None of these

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Ans.d

Let the number = x.

45 × 38x = 24 or x = $\frac{24 \times 2 \times 5}{3} = 80$

∴ 250 per cent of the number = 250100 × 80 = 200

7. What approximate value should come in place of the question mark (?) in the following equation?
159% of 6531.8 + 5.5 × 1015.2 = ? + 5964.9
(a) 10,000
(b) 10,900
(c) 11,000
(d) 10,600
(e) 12,000

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Ans.a

? ≈ 160% of 6530 + 5.5 × 1010 – 5965

≈ 10448 + 5555 – 5965 ≈ 10,000

8. When 35 per cent of a number is added to another number,the second number increases by its 20 per cent. What is the ratio between the second number and the first number?
(a) 4 : 7
(b) 7 : 4
(c) 8 : 5
(d) Data inadequate
(e) None of these

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Ans.b

35% of x + y = 120100y

or $\frac{35x \; + \; 100y}{100} = \frac{120y}{100} \Rightarrow 35x = 20y$

yx = 3520 = 7 : 4

9. Two-fifths of thirty per cent of one-fourth of a number is 15. What is 20 per cent of that number?
(a) 90
(b) 150
(c) 100
(d) 120
(e) None of these

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Ans.c

Let the number = x

25 × 30100 × x4 = 15

or $x = \frac{15 \times 5 \times 100}{2 \times 30} = 500$

20% of 500 = 100

10. Jeevan bought an article with 30 per cent discount on the labelled price. He sold the article with 12 per cent profit on the labelled price. What was his per cent profit on the price he bought?
(a) 40
(b) 50
(c) 60
(d) Data inadequate
(e) None of these

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Ans.c

Let the labelled price of the article = ₹ 100 then

CP = ₹ 70 and SP = ₹ 112.

∴ Read profit percent = $\frac{112 - 70}{70} \times 100$

= $\frac{42}{7} \times 10 = 60$