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

Question : 21 [SSC CAPFs SI 2013]

If the square of the sum of two numbers is equal to 4 times of their product, then the ratio of these numbers is :

a) 1 : 1

b) 1 : 2

c) 1 : 3

d) 2 : 1

Answer: (a)

$(x + y)^2 = 4xy$

$x^2 + y^2 + 2xy - 4xy = 0$

$(x - y)^2$ = 0 ⇒ x = y

x : y = 1 : 1

Question : 22 [SSC CPO S.I.2003]

The sum of three numbers is 116. The ratio of second to the third is 9 : 16 and the first to the third is 1 : 4. The second number is

a) 34

b) 36

c) 32

d) 30

Answer: (b)

NumberIIIIII
9:16
4:1
36:64:16
9:16:4

Therefore, second number

=$9/{9 +16+4}×116$

=$9/29×116=36$

Question : 23 [SSC CGL Prelim 2002]

The ratio of two numbers is 10 : 7 and their difference is 105. The sum of these numbers is

a) 1190

b) 1610

c) 805

d) 595

Answer: (d)

Let the nos. be 10x & 7 x then,

10 x - 7x = 105

3x = 105 ⇒ x = 35

Sum = 10x + 7x = 17x

= 17 × 35 = 595

Question : 24 [SSC CGL Tier-I 2016]

Two numbers are in the ratio 3 : 5. If 6 is added to each of them, the ratio becomes 2 : 3. The numbers are

a) 24 and 40

b) 18 and 30

c) 30 and 50

d) 21 and 35

Answer: (b)

Let the numbers be 3x and 5x.

According to the question,

${3x + 6}/{5x + 6}= 2/3$

10x + 12 = 9x + 18

10x - 9x = 18 - 12

x = 6

Numbers are :

3x = 3 × 6 = 18 and

5x = 5 × 6 = 30

Question : 25 [SSC CGL Tier-II 2013]

Three numbers are in the ratio 2 : 3 : 4. If the sum of their squares is 1856, then the numbers are

a) 12, 18 and 24

b) None of the above

c) 16, 24 and 32

d) 8, 12 and 16

Answer: (c)

Numbers = 2x, 3x and 4x

$(2x)^2 + (3x)^2 + (4x)^2$ = 1856

$4x^2 + 9x^2 + 16x^2$ = 1856

$29x^2$ = 1856

$x^2$ = 1856 ÷ 29 = 64

$x = √64$ = 8

Numbers = 16, 24 and 32

IMPORTANT quantitative aptitude EXERCISES

type 3 addition subtraction product on ratio & proportion Online Quiz

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