# Understand the concept of ratio and proportion

Posted: Date Posted – 11:49 PM, Thu – Sep 22, 22 Here are some practice questions along with solutions that will help you in your preparation for the state government recruitment tests. Here are some practice questions along with solutions that will help you in your preparation for the state government recruitment tests.

Hyderabad: This article follows the last article on the subject of ratios and proportions. Here are some practice questions along with solutions that will help you in your preparation for the state government recruitment tests.

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

Solution: Number required = x

∴ (11 – x) / (15 – x) = 2/3

=> ; 33 – 3x = 30 – 2x

=> ; 3x – 2x = 33 – 30
=> ; x = 3
2. Two numbers are in the ratio 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

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

According to the questions,

=> ; 69x – 207 = 60x – 108

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

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

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

Number of daughters = 4/9 × 432 = 192

Let x be the new number of daughters.

According to the question,

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

=> ; 252 / (192x) = 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, while the average of 9 of them is 34. If the two remaining numbers are in the ratio of 2:3, find the value of the smallest number (between the two remaining numbers).
a) 18 b) 36 c) 54 d) 72
Solution: Depending on the question,
Sum of the remaining two numbers
= 11 × 36 – 9 × 34
= 396 – 306 = 90
Ratio of the remaining two numbers = 2:3
 Smallest 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

Solution: Consider the numbers x and 5x.

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

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

Director
MVK Publications
Dilsukhnagar
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