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 : 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

The correct answers to the above question in:

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.

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

Question : 1

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 : 2

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 : 3

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 : 4

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 : 5

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

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

Question : 6

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

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