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
Hence, 7x+x = 28+4 = 32 years
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
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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
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
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.
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Ex:5 The ratio of the present ages of Ekta and Ankita is respectively 3:2. After 8 years, the ratio of their ages will be 11:8. What will be the present age of Ekta’s son if his age is half of the present age of Ankita?
(1) 12 years (2) 24 years (3) 18 years (4) 9 years (5) None of these
Sol: Ekta age = 3x years
Ankita’s age = 2x years
After 8 years,
3x+8 / 2x+8 = 11/8
So, 24x + 64 = 22x + 88
Or, 2x = 88 – 64 = 24 or,x = 12
So,Ankita’s age = 2x = 2 × 12 = 24 years
and,age of Ekta’s son = 1/2× 24 = 12 years
Ex:6 The ratio between the ages of a father and a son at present is 5:2 respectively. Four years hence the ratio between the ages of the son and his mother will be 1:2 respectively. What is the ratio between the present ages of the father and the mother respectively?
(1) 3:4 (2) 5:4 (3) 4:3 (4) cannot be determined (5) None of these
[SBI PO PRE 2016]
Sol: F/S =5x/2x
S+4/M+4 = 2x+4/m+4 = ½
M+4 = 4x+8
M = 4x+4
So, F/M= 5x/ 4x+4
Hence, answer cannot be determined
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