Grasp ratio & proportion concept well

Here are some practice questions along with solutions that will help you in your preparation for the State government recruitment tests.

Hyderabad: This article is in continuation to the last article focusing on the ratio and proportion topic. Here are some practice questions along with solutions that will help you in your preparation for the State government recruitment tests.

1. What number should be subtracted from both the terms of the ratio 11 : 15 so as to make it as 2 : 3?
a) 3 b) 1 c) 5 d) 6

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Ans: a

Solution: Required number = x

∴ (11 – x) / (15 – x) = 2/3

=>; 33 – 3x = 30 – 2x

=>; 3x – 2x = 33 – 30
=>; x = 3
2. Two numbers are in the ratio of 3 : 5. If 9 is subtracted from each, then they are in the ratio 12 : 23. The smaller number is?

a) 25 b) 33 c) 82 d) 46

Ans: b

Solution: Numbers = 3x and 5x (let)

According to question,

=>; 69x – 207 = 60x – 108

=>; 69x – 60x = 207 – 108
=>; 9x = 99
=>; x = 99/9 = 11
 Smaller number = 3x
= 3 × 11 = 33

3. The ratio of number of boys to the number of girls in a school of 432 pupils is 5 : 4. When some new boys and girls are admitted, the number of boys increase by 12 and the ratio of the boys to girls changes to 7 : 6. The number of new girls admitted is ___?
a) 23 b) 19 c) 15 d) 24

Ans: d

Solution: Original number of boys in school = 5/9 × 432 = 240

Number of girls = 4/9 × 432 = 192

Let the new number of girls be x.

According to the question,

=>; (240 12) / (192 x) = 7/6

=>; 252 / (192 x) = 7/6
=>; 192 × 7 7x = 252 × 6

=>; 1344 7x = 1512

=>; 7x = 1512 – 1344 = 168

=>; x = 168/7 = 24

4. The average of 11 numbers is 36, whereas average of 9 of them is 34. If the remaining two numbers are in the ratio of 2 : 3, find the value of the smaller number (between remaining two numbers).
a) 18 b) 36 c) 54 d) 72
Ans: b
Solution: According to the question,
Sum of remaining two numbers
= 11 × 36 – 9 × 34
= 396 – 306 = 90
Ratio of the remaining two numbers = 2 : 3
 Smaller number = 2/5 × 90 = 36
5. If the ratio of two numbers is 1 : 5 and their product is 320, then the difference between the squares of these two numbers is?
a) 1536 b) 1356 c) 1236 d) 1336

Ans: a

Solution: Let the numbers be x and 5x.

According to the question,
x × 5x = 320
=>; 5×2 = 320
=>; x2 = 320/5 = 64
=>; x = √64 = 8
 Required difference
= (5x)2 – x2
= 25×2 – x2 = 24×2

= 24 × 8 × 8 = 1536
To be continued…
M Venkat

Director
MVK Publications
Dilsukhnagar
7671002120