# Problems on ages

Quantitative Aptitude Questions, particularly Problems on Ages, are among the most frequently asked questions in all competitive exams at all levels. The questions concerning this topic may appear to be confusing and complicated, but once a candidate grasps the concept, they can easily score points. Learn to solve the tricky questions based on the ages given below!

1. 20 years ago Ram was half of Raju in age. If the ratio of their present ages is 3 : 4, what will be the total of their present ages?

Let Ram's age 20 years ago = x years

Raju's age 20 years ago = 2x years

$\frac{(x + 20) }{ (2x+ 20)} = \frac{3}{4}$

4x + 80 = 6x + 60

x = 10
The total of their present ages =(x + 20 + 2x + 20)

= (3x + 40)

= 3$\times$10+40 = 70 years.

1. A is three years older than B who is twice as old as C. If the total of the ages of A, B and C be 33, the how old is C?

Let C's age be x years.

B's age = 2x years.

A's age = (2x + 3) years.

(2x + 3) + 2x + x =33 5x =30

x = 6. Hence, C's age =x =6 years.

1. The ratio of Vimal's age and Amala's age is in the ratio $3 : 5$ and the sum of their age is $80$ years. The ratio of their ages after $10$ years will be _

• Let their ages be $3x : 5x.$ $3x + 5x = 80;\ 8x = 80.$ $\therefore\ x= 10.$
• Ratio of their age after $10$ years $= (3x + 10): (5x + 10) = 40 : 60.$ $= 2 : 3.$
• Answer is $2:3$
1. The ratio of ages of A and B is 23 : 19 . Their sum of ages is 63 years. Find their difference of ages ?

$Ratio\:of\:ages=\:23\::\:19\\\\ Sum\:of\:ages=\:63\:years\\\\ \therefore \:\:23+19=\:42\:ratio=\:63\:years\\\\ 1\:ratio=\:\frac{63}{42}=\:1.5\:years\\\\ Difference\:in\:ratios=\:23-19=\:4\:ratio\\\\ Difference\:in\:ages=\:4\times 1.5=\:6\:years$

1. The present age of three persons are in the proportion of 5 : 8 : 7. Ten years ago, the sum of their ages was 96. Find the present age of the youngest person.

Let present age of three persons be 5x, 8x & 7x.

10 years ago their ages were,

5x – 10, 8x – 10 & 7x – 10

Sum of their ages = 96

(5x – 10) + (8x – 10) + (7x – 10) = 96

20x = 126

x = 6 .3

the ages are 5x, 8x, 7x = 31.5,50.4 , 44.1.

age of the youngest is 31.5 ~ 31 years.