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

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__PROBLEMS ON AGES__

__PROBLEMS ON AGES__

‘The Problems 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: **Problems on Ages** **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 7 x and x years respectively.**

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

Age of son = (*x *+ 4) years

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

So, 7*x *+ 4 = 4*x *+ 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)**

**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**/**7*x* 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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**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 = 3*x *years

Ankita’s age = 2*x *years

After 8 years,

3x+8** /** 2x+8 = 11/8

So, 24*x *+ 64 = 22*x *+ 88

Or, 2*x *= 88 – 64 = 24 or,*x *= 12

So,Ankita’s age = 2*x *= 2 × 12 = 24 years

and,age of Ekta’s son = 1/2× 24 = 12 years

**Ans: (1)**

**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

**Ans: (4)**

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