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

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

Questions : Three numbers are in the ratio 5:7:12. If the sum of the first and the third numbers is greater than the second number by 50. The sum of the three numbers is

(a) 95

(b) 85

(c) 120

(d) 125

The correct answers to the above question in:

Answer: (c)

Let the numbers be 5x, 7x and 12x.

According to the question,

5x + 12x = 7x + 50

17x - 7x = 50

10x = 50

$x = 50/10$ = 5

Required sum

= 5x + 7x + 12x = 24x

= 24 × 5 = 120

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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 68. If the ratio of the first to the second be 2 : 3 and that of the second to the third be 5 : 3, then the second number is

a) 20

b) 48

c) 58

d) 30

Answer: (d)

Let the numbers be a, b and c.

Then a : b = 2 : 3

b : c = 5 : 3

a : b : c = 2×5 : 3×5 : 3×3

= 10 : 15 : 9

Let the numbers now be 10x, 15x and 9x

10 x + 15x + 9x = 68

34x = 68

$x = 68/34 = 2$

Second number = 15 x

= 15 × 2 = 30

Question : 2

In a 45 litres mixture of milk and water, the ratio of the milk to water is 2 : 1. When some quantity of water is added to the mixture, this ratio becomes 1 : 2. The quantity of water added is

a) 35 litres

b) 45 litres

c) 21 litres

d) 10 litres

Answer: (b)

Quantity of milk in 45 litres

= $2/3$ × 45 = 30 litres.

Water = (45 - 15) = 15 litres

Let x litres of water be added.

$30/{15 + x} = 1/2$

15 + x = 60

x = 60 - 15 = 45 litres.

Question : 3

The ratio between a two - digit number and the sum of the digits of that number is 4 : 1. If the digit at the unit’s place is 3 more than the digit at the ten's place, then the number is

a) 36

b) 25

c) 69

d) 47

Answer: (a)

Check through options

Number = 36

3 + 6 = 9; 6 - 3 = 3

and 36 : 9 = 4 : 1

Otherwise - 10x + y : x + y = 4 : 1

10x + (x + 3) : x + (x + 3) = 4 : 1

${11x + 3}/{2x + 3} = 4/1$

11x + 3 = 8x + 12

3x = 9

x = 3 and y = 6

Then the number is 36.

Question : 4

Four numbers are in the ratio 1 : 2 : 3 : 4. Their sum is 16. The sum of the first and fourth number is equal to :

a) 10

b) 80

c) 8

d) 5

Answer: (c)

x + 2x + 3x + 4x = 16

$x = 16/10$ = 1.6

Sum = 1.6 + 6.4 = 8

Question : 5

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

Question : 6

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

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