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 : 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

The correct answers to the above question in:

Answer: (a)

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

Then, 5 years ago,

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

3x - 15 = 2x - 5

x = 15 - 5 = 10

Age of elder brother

= 10 × 2 = 20

Required ratio

= ${10 + 5}/{20 + 5} = 15/25$ = 3 : 5

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Question : 1

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

Question : 2

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 : 3

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 : 4

Harsha is 40 years old and Ritu is 60 years old. How many years ago was the ratio of their ages 3:5?

a) 37 years

b) 5 years

c) 20 years

d) 10 years

Answer: (d)

Let x years ago the ratio of their age was 3 : 5

According to the question

${40 - x}/{60 - x}= 3/5$

200 - 5x = 180 - 3x

2x = 20

x = 10 years

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