type 2 age based ratio & proportion problems 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 : At present, the ratio of the age of Maya and Chhaya is 6 : 5 and fifteen years from now, the ratio will get changed to 9 : 8. Maya’s present age is

(a) 30 years

(b) 40 years

(c) 24 years

(d) 21 years

The correct answers to the above question in:

Answer: (a)

Let Maya’s present age be 6x years and Chhaya’s present age be 5x years.

After 15 years,

${6x + 15}/{5x + 15} = 9/8$

48x + 120 = 45x + 135

48x - 45x = 135 - 120

3x = 15 ⇒ x = 5

Maya’s present age = 6x

= 6 × 5 = 30 years

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Read more age based ratio and proportion problems Based Quantitative Aptitude Questions and Answers

Question : 1

My grandfather was 9 times older than me 16 years ago. He will be 3 times of my age 8 years from now. Eight years ago, the ratio of my age to that of my grandfather was

a) 1 : 2

b) 1 : 5

c) 2 : 5

d) 3 : 8

Answer: (b)

16 years ago,

My age = x years

My grandfather’s age = 9x years

After 8 years from the present,

9x + 16 + 8 = 3(x + 8 + 16)

9x + 24 = 3x + 24 + 48

9x + 24 = 3x + 72

9x - 3x = 72 - 24

6x = 48

$x = 48/6$ = 8

Required ratio 8 years ago,

= (x + 8) : (9x + 8)

= (8 + 8) : (9 × 8 + 8)

= 16 : 80 = 1 : 5

Question : 2

The ratio of A’s age to B’s age is 4 : 3. ‘A’ will be 26 years old after 6 years. The age of B now is :

a) 21 years

b) 15 years

c) 12 years

d) 19$1/2$ years

Answer: (b)

A’s present age

= 4x years (let).

According to the question,

4x + 6 = 26

4x = 26 - 6 = 20

$x = 20/4$ = 5

B’s present age

= 3x = 3 × 5 = 15 years

Question : 3

The ratio of the ages of a father and his son 10 years hence will be 5 : 3, while 10 years ago, it was 3:1. The ratio of the age of the son to that of the father today, is

a) 2 : 3

b) 2 : 5

c) 1 : 3

d) 1 : 2

Answer: (d)

Let the age of father 10 years hence is 5x years,

then age of son 10 years hence will be 3x years.

According to the question,

${5x - 10 - 10}/{3x - 10 - 10} = 3/1$

${5x - 20}/{3x - 20} = 3/1$

5x - 20 = 9x - 60

4x = 40 or x = 10

Required ratio

= (3x - 10) : (5x - 10)

= 20 : 40 = 1 : 2

Question : 4

The ratio of the age of a father to that of his son is 5: 2. If the product of their ages in years is 1000, then the father's age (in years) after 10 years will be :

a) 80

b) 100

c) 60

d) 50

Answer: (c)

Let father’s age be 5x years.

Son’s age = 2x years

5x × 2x = 1000

$x^2$ = 100 ⇒ x = 10

Father’s age after 10 years

= 5x + 10

= 5 × 10 + 10 = 60 years

Question : 5

The average age of boys in the class is twice the number of girls in the class. The ratio of boys and girls in the class of 50 is 4 : 1. The total of the ages (in years) of the boys in the class is

a) 800

b) 400

c) 2500

d) 2000

Answer: (a)

Boys in class = $4/5 × 50$ = 40

Girls = $1/5 × 50$ = 10

Average age of boys

= 10 × 2 = 20 years

Total age of boys

= 20 × 40 = 800 years

Question : 6

The ratio of present age of two brothers is 1 : 2 and 5 years back the ratio was 1 : 3. What will be the ratio of their age after 5 years ?

a) 3 : 5

b) 5 : 6

c) 2 : 3

d) 1 : 4

Answer: (a)

Let the present age of two brothers be x and 2x years.

Now, ${x - 5}/{2x - 5} =1/3$

3x - 15 = 2x - 5

3x - 2x = 15 - 5

x= 10

Their present age

= 10 and 20 years

After 5 years their required ratio

= $15/25 = 3/5$ = 3 : 5

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