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

Question : 26 [SSC CPO S.I.2009]

The two numbers are in the ratio 2 : 3 and their product is 96. The sum of the numbers is

a) 101

b) 102

c) 20

d) 5

Answer: (c)

Let the numbers be 2x and 3x.

2x × 3x = 96

$x^2 = 96/6$ = 16

$x = √16$ = 4

Sum = 2x + 3x = 5x

= 5 × 4 = 20

Question : 27 [SSC CGL Tier-II 2014]

The sum of two numbers is equal to 20 and their difference is 25. The ratio of the two numbers is

a) 3 : 5

b) 2 : 7

c) 7 : 9

d) 9 : 1

Answer: (d)

Numbers are x and y

x + y = 25

x - y = 20

On adding,

2x = 45

$x = 45/2$ = 22.5

From equation (i),

22.5 + y = 25

y = 25 - 22.5 = 2.5

Required ratio

= 22.5 : 2.5 = 9 : 1

Question : 28 [SSC CGL Prelim 2000]

The sum of two numbers is 40 and their difference is 4. The ratio of the numbers is :

a) 11 : 9

b) 11 : 18

c) 22 : 9

d) 21 : 19

Answer: (a)

Let the two numbers be x and y.

According to question,

x + y = 40 ...(i)

x - y = 4 …(ii)

From equation (i) and (ii), we get

x = 22 and y = 18

Required ratio

= $22/18 = 11/9$ = 11 : 9

Question : 29 [SSC CGL Prelim 2000]

What number should be subtracted from both terms of the ratio 15 : 19 in order to make it 3 : 4 ?

a) 5

b) 3

c) 6

d) 9

Answer: (b)

Let x be subtracted from each term of $15/19$.

${15 - x}/{19 - x} = 3/4$

57 - 3x = 60 - 4x

x = 3

Question : 30 [SSC CPO S.I.2009]

Three numbers are in the ratio 5 : 6 : 7. If the product of the numbers is 5670, then the greatest number is

a) 21

b) 28

c) 18

d) 15

Answer: (a)

Let the numbers be 5x, 6x and 7x respectively.

5x × 6x × 7x = 5670

$x^3 = 5670/{5 × 6 × 7} = 27$

x = $√^3{27}$= 3

The greatest number = 7x

= 7 × 3 = 21

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