Question

Aman’s age is three times his son’s age. Ten years ago he was five times his son’s age. Find their present ages.
$A.$ Aman’s age: 90 years; Aman’s sons age: 30 years
$B.$ Aman’s age: 45 years; Aman’s sons age: 15 years
$C.$ Aman’s age: 60 years; Aman’s sons age: 20 years
$D.$ Aman’s age: 75 years; Aman’s sons age: 25 years

Answer 1

Hint – Here we will proceed by forming two equations and then try to solve them simultaneously by applying the conditions given in the question.

Complete Step-by-Step solution:
Let Aman’s sons present age = $x$
Then, Aman’s present age = $3x$
Ten years ago,
Aman’s age $ = 3x - 10$
Aman’s son’s age$ = x - 10$
It is given that,
Ten years ago, he was five times his son’s age
Aman’s age $ = 5 \times $Aman’s son’s age
$3x - 10 = 5\left( {x - 10} \right)$
$3x - 10 = 5x - 50$
$3x - 10 + 50 = 5x$
$3x + 40 = 5x$
$40 = 5x - 3x$
$40 = 2x$
$x = \dfrac{{40}}{2}$
$x = 20$
Hence,
Aman’s Son’s age $ = x = 20years$
Aman’s age$ = 3x = 3 \times 20 = 60years$

Note – In order to solve such types of questions, one must remember the difference between their ages is the constant variable so we have to find a multiple of three that when added 10 will be an even number. Other methods to solve these types of questions are transposing the equations, substitution method and by L.H.S. and R.H.S. approach.