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 : 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

The correct answers to the above question in:

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

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

Question : 1

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 : 2

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 : 3

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 : 4

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 : 5

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 : 6

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

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