type 3 addition subtraction product on ratio & proportion Section-Wise Topic Notes With Detailed Explanation And Example Questions

MOST IMPORTANT quantitative aptitude - 9 EXERCISES

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The following question based on ratio & proportion topic of quantitative aptitude

Questions : 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

The correct answers to the above question in:

Answer: (a)

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

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

$(x - y)^2$ = 0 ⇒ x = y

x : y = 1 : 1

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Read more addition subtraction product on ratio and proportion Based Quantitative Aptitude Questions and Answers

Question : 1

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 : 2

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 : 3

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 : 4

Three numbers are in the ratio 3 : 4 : 5. The sum of the largest and the smallest equals the sum of the second and 52. The smallest number is

a) 39

b) 52

c) 27

d) 20

Answer: (a)

Let the numbers be 3x, 4x and 5x.

5x + 3x = 4x + 52

4x = 52 ⇒ x =13

The smallest number

= 3x = 3 × 13 = 39

Question : 5

Two numbers are in the ratio 1 : 3. If their sum is 240, then their difference is

a) 100

b) 96

c) 108

d) 120

Answer: (d)

Let the numbers be 3x and x,

Then, 3x + x = 240

4x = 240

$x = 240/4$ = 60

Difference = 3x - x = 2x

= 2 × 60 = 120

Question : 6

If A and B are in the ratio 4 : 5 and the difference of their squares is 81, what is the value of A ?

a) 36

b) 15

c) 12

d) 45

Answer: (c)

Let A = 4x and B = 5x.

According to the question,

$(5x)^2 - (4x)^2$ = 81

$25x^2 - 16x^2$ = 81

$9x^2 = 81 ⇒ x^2$ = 9

$x = √9$ = 3

A = 4x = 4 × 3 = 12

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