Problems Based on Ages – Techniques and solutions

Problems on Ages – Techniques to Solve Quickly For IBPS/RRB/SBI Exam

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PROBLEMS ON AGES

‘The Problem on Ages’ is one of the easiest chapters of quantitative aptitude questions of which students can solve in a fraction of seconds using tricks and shortcuts explained below. Before starting you should go through the basic concept of solving linear equations which will be used here.

Have a look at the following questions:

Ex:1 – The ratio of the ages of the mother and the son at present is 7:1. After 4 years, the ratio will become 4:1. What is the sum of the present ages of the mother and the son?

(1) 28 years          (2) 37 years                 (3) 32 years                    (4) 36 years              (5) None of these

Sol: Let the present age of mother and son be 7x and x years respectively.

After 4 years, age of mother = (7x + 4) years

Age of son = (x + 4) years

Given, 7x+4/x+4 = 4/1

So, 7x + 4 = 4x + 16

3x=12

So, x=4

Hence, 7x+x = 28+4 = 32 years

Ans(3)      

Ex:2 The average age of Rahul and Sahil is 20 years. If Mohit were to replace Rahul, the average would be 19 years and if Mohit were to replace Sahil, the average would be 21 years. What are the ages of Rahul, Sahil, and Mohit respectively (in years)?

(1) 22, 18, 20          (2) 18, 22, 20       (3) 22, 20, 18          (4) 18, 20, 22             (5) None of these

Sol: Rahul + Sahil = 40 years……… (i)

Mohit + Sahil = 38 years…….. (ii)

Rahul + Mohit = 42 years…….. (iii)

Solving (i) (ii) and (iii), we get

Rahul = 22 years,     Sahil = 18 years and Mohit = 20 years

Ans: (1)

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Ex:3 The average age of the family of five members is 24 years. If the present age of the youngest member is 8 years, then what was the average age of the family at the time of the birth of the youngest member?

(1) 22 years                 (2) 16 years                 (3) 19 years                 (4) 18 years                   (5) 25 years

Sol: Total age of 5 member family = 24 × 5 = 120 years

Total age 8 years ago = 120 – (5 × 8) = 80 years

So, required average age = 80/5= 16 years

Ans: (2)

Ex:4 Aman’s present age is 2/7 of his father’s present age. Aman’s brother is 3 years older than him. The ratio between the present age of Aman’s father and Aman’s brother is 14:5. What is Aman’s present age?

(1) 6 years               (2) 15 years                  (3) 12 years                (4) 18 years                         (5) 20 year

Sol: Let the present age of Aman’s father be x years.

Then, Aman’s age = 2/7x years

Aman’s brother’s age = 2/7x +3

= 2x+21/7

Now ratio between the present age of Aman’s father and that of Aman’s brother = 7x/2x+21=14/5

Or, x/2x+21= 2/5

Or, x = 42 years

So, Aman’s present age = 42 × 2/7 = 12 years.

Ans: (3)

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