type 7 finding sum difference product based ratio & proportion problems Practice Questions Answers Test with Solutions & More Shortcuts

Question : 26 [SSC CGL Tier-I 2014]

What number should be subtracted from both the terms of the ratio 11 : 15 so as to make it as 2 : 3 ?

a) 4

b) 5

c) 3

d) 2

Answer: (c)

Required number = x

${11 - x}/{15 - x} = 2/3$

33 - 3x = 30 - 2x

3x - 2x = 33 - 30

x = 3

Question : 27 [SSC CGL Tier-I 2016]

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) 1435

c) 1256

d) 1024

Answer: (a)

Let the numbers be x and 5x.

According to the question,

x × 5x = 320

$5x^2$ = 320

$x^2 = 320/5$ = 64

$x = √64$ = 8

Required difference

= $(5x)^2 - x^2$

= $25x^2 - x^2 = 24x^2$

= 24 × 8 × 8 = 1536

Question : 28 [SSC CGL Tier-1 2011]

What number should be added to or subtracted from each term of the ratio 17 : 24 so that it becomes equal to 1 : 2 ?

a) 7 is added

b) 10 is subtracted

c) 10 is added

d) 5 is subtracted

Answer: (b)

Let the number x be added.

${17 + x}/{24 + x} = 1/2$

34 + 2x = 24 + x

2x - x = 24 - 34

x = - 10

Hence, 10 should be subtracted.

Question : 29 [SSC CGL Tier-II 2016]

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) 24

b) 20

c) 14

d) 12

Answer: (a)

Original number of boys in school

= $5/9$ × 432 = 240

Number of girls

= 432 - 240 = 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

Question : 30 [SSC Investigator 2010]

Two numbers are in the ratio 3 : 5. If each number is increased by 10, the ratio becomes 5 :7. The smaller number is

a) 15

b) 25

c) 12

d) 9

Answer: (a)

Let the numbers be 3x and 5x.

${3x + 10}/{5x + 10} = 5/7$

25x + 50 = 21x + 70

4x = 20 ⇒ x = 5

Smaller number

= 3x = 3 × 5 = 15

Using Rule 34,

Here, a = 3, b = 5, c = 5, d = 7, x = 10

Smallest number = ${xa(c-d)}/{ad-bc}$ a < b

= ${10 × 3(5 - 7)}/{3 × 7 - 5 × 5}$

= ${- 60}/{21 - 25} = 60/4$ = 15

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