Question

The sum of the ages of two friends Avish and Lakhan 14 years ago was one-third of the sum of their present ages. If the present age of Avish is Four-third the present age of Lakhan, then what is the present age of Lakhan? (in years)

Answer 1

Hint: Let the present age of Avish and Lakhan be a, b respectively and then solve the equation as given in the question to find their present age.

Complete step by step solution: This is an age-based problem given for two friends Avish and Lakhan. I here present ages are unknown to us and we are asked to find their present age. Let us assume that the present age of Avish = a:
and the present age of Lakhan = b;
Now, given that 14 years ago, the sum of their ages was equal to one-third of the sum of their present age.
So, Avish’s age, 14 years ago = (present age)− (14 years)
                    = a - 14
And, Lakhan’s age, 14 years ago = (present age) – (14 years)
                    = b – 14
So, According to questions;
$\left( {a - 14} \right) + \left( {b - 14} \right) = \dfrac{{a + b}}{3}$
\[ \Rightarrow a - 14 + b - 14 = \dfrac{{a + b}}{3}\]
$ \Rightarrow a + b - 28 = \dfrac{{a + b}}{3}$
\[ \Rightarrow 3a + 3b - \left( {28 \times 3} \right) = a + b\]
$ \Rightarrow 3a + 3b - 84 = a + b$
$ \Rightarrow 3a + 3b - a - b = 84$
$ \Rightarrow 2a + 2b = 84$
$ \Rightarrow 2\left( {a + b} \right) = 84$
$ \Rightarrow a + b = 42$ ①
Again, as mentioned in question;
Present age of Avish = four– third of the present age of Lakhan
$ \Rightarrow a = \dfrac{4}{3}b$ ②
Substituting equation ② in equation ① ;
$ \Rightarrow a + b = 42$
$ \Rightarrow \dfrac{4}{3}b + b = 42$
$ \Rightarrow \dfrac{{4b + 3b}}{3} = 42$
$ \Rightarrow 7b = \left( {42 \times 3} \right) = 126$
$ \Rightarrow b = \dfrac{{126}}{7} = 18$
$\therefore $ present age of Lakhan = b = 18 years
and present age of Avish $ = a = \dfrac{4}{3}b$
$ = \dfrac{4}{3} \times 18 = 24{\text{years}}$

Note: If the present age of a person is x, then the person’s age before some years let’s say before 10 years would be $\left( {x - 10} \right)$ years. In the same way, we have to solve the given question.