Solved Aptitude Question: Find Age Based On Given Ratios

Age Problem

Dear Reader, in this question you will be given ratios between ages of three people. You have to find the age of a given person.

Example Question:
Find the age of R. The ratio between ages of Q and R is 3:4. R is twice as old as P. Sum of their ages is 45.

Here’s How To Solve This Problem:
In this problem, we have to solve three ages i,e three variables P, Q and R. To solve three unknowns we need to have at least three equations. Based on the conditions given we have to form the equations and solve them to arrive at the answer.

Solution:
Condition i:
The ratio between Q and R is 3:4.
Or q/r = 3/4
q = 3r/4 … (1)

Condition ii:
R is twice as old as P
r = 2p
p = r/2 …(2)

Condition iii:
Sum of the ages is 45
p + q + r = 45 …(3)

Let us now solve the equations 1, 2 and 3
If we substitute the values of q and p from equations 1 and 2 in equation 3, we will get
3r/4 + r/2 + r = 45
3r + 2r + 4r / 4 = 45
9r =180
r = 20
Therefore, the age of R = 20 years.

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