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

Question : 36 [SSC CGL Prelim 1999]

The ratio of two numbers is 3 : 8 and their difference is 115. The smaller of the two numbers is :

a) 69

b) 59

c) 194

d) 184

Answer: (a)

Let the numbers be 3x and 8x.

8x - 3x = 115

5x = 115

$x = 115/5$ = 23

The smaller number

= 3x = 3 × 23 = 69

Question : 37 [SSC CGL Tier-II 2015]

If the product of two positive numbers is 1575 and their ratio is 7 : 9, then the greater number is

a) 135

b) 63

c) 35

d) 45

Answer: (d)

Numbers = 7x and 9x (let)

According to the question,

7x × 9x = 1575

$x^2 = 1575/{7 × 9}$ = 25

$x = √25$ = 5

Larger number = 9x

= 9 × 5 = 45

Question : 38 [SSC CGL Prelim 2005]

Three numbers are in the ratio $1/2 : 2/3 : 3/4$. The difference between the greatest and the smallest number is 36. The numbers are

a) 72, 84, 96

b) 72, 96, 108

c) 60, 72, 96

d) 72, 84, 108

Answer: (b)

Ratio of numbers

= $1/2 : 2/3 : 3/4$

= $1/2 × 12 : 2/3 × 12 : 3/4 ×12$

= 6 : 8 : 9

Let the numbers be 6x, 8x and 9x.

Now, 9x - 6x = 36

x = 12

Numbers are 72, 96 and 108.

Question : 39 [SSC FCI Ass Grade-III 2012]

The average of two numbers is 62. If 2 is added to the smallest number, the ratio between the numbers becomes 1 : 2. The difference of the numbers is

a) 84

b) 44

c) 40

d) 62

Answer: (b)

Average of two no's = 62

Sum of the numbers

= 62 × 2 = 124

Sum of the numbers = 124

If the larger number be x,

then smaller number = 124 - x

${124 - x + 2}/{x} =1/2$

252 - 2x = x

3x = 252 ⇒ x = 84

Smaller number

= 124 - 84 = 40

∴ Difference = 84 - 40 = 44

Question : 40 [SSC CPO S.I.2003]

The sum of three numbers is 98. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8, then the second number is

a) 30

b) 20

c) 48

d) 49

Answer: (a)

Let the numbers be x, y and z.

Then x : y = 2 : 3 ; y : z = 5 : 8

x : y : z = 2 × 5 : 3 × 5 : 3 × 8

= 10 : 15 : 24

Sum of the ratios

= 10 + 15 + 24 = 49

The second number

= $15/49$ × 98 = 30

IMPORTANT quantitative aptitude EXERCISES

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