type 3 addition subtraction product on ratio & proportion Practice Questions Answers Test with Solutions & More Shortcuts

Question : 11 [SSC CGL Tier-I 2016]

Two numbers whose sum is 84 can not be in the ratio

a) 1 : 3

b) 3 : 2

c) 13 : 8

d) 5 : 7

Answer: (b)

According to the question,

The number 84 must be a multiple of sum of the terms of ratio.

For ratio 3 : 2,

Sum of the terms of ratio

= 3 + 2 = 5

which is not a factor of 84.

Question : 12 [SSC CHSL 2014]

The ratio of three positive numbers is 2 : 3 : 5 and the sum of their squares is 608. The three numbers are

a) 8, 12, 20

b) 4, 6, 10

c) 10, 15, 25

d) 2, 3, 5

Answer: (a)

Numbers = 2x, 3x and 5x,

According to question,

$(2x)^2 + (3x)^2 + (5x)^2$ = 608

$4x^2 + 9x^2 + 25x^2$ = 608

$38x^2$ = 608

$x^2 = 608/38$ = 16

$x = √16$ = 4

Numbers ⇒ 2x = 2 × 4 = 8

3x = 3 × 4 = 12

5x = 5 × 4 = 20

Question : 13 [SSC CGL Prelim 2002]

The product of two positive integers is 1575 and their ratio is 9 : 7. The smaller integer is

a) 45

b) 70

c) 35

d) 25

Answer: (c)

Let the integers be 9x and 7x respectively.

According to the question,

9x × 7x = 1575

$x^2 = 1575/63$

$x^2 = 25 ⇒ x = 5

[x being positive (+ve) integer]

Smaller integer

= 7x = 7 × 5 = 35

Question : 14 [SSC CGL Tier-I 2013]

The ratio of number of balls in bags x,y is 2 : 3. Five balls are taken from bag y and are dropped in bag x. Number of balls are equal in each bag now. Number of balls in each bag now is

a) 30

b) 25

c) 20

d) 45

Answer: (c)

Number of balls in bag x and y respectively

= 2a and 3a

3a - 5 = 2a + 3

a = 5 + 3 = 8

Total number of balls

= 5a = 40

Balls in each bag = 20

Question : 15 [SSC CHSL 2014]

Two numbers are in the ratio of 2 : 3. If their sum is 125, find the numbers.

a) 20, 30

b) 32, 78

c) 24, 36

d) 50, 75

Answer: (d)

Ratio of numbers = 2 : 3

Sum of ratios = 2 + 3 = 5

First number = $2/5 × 125$ = 50

Second number = $3/5 × 125$ = 75

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