Question

Ali’s age is 5 times that of Nitesh. After 9 years Ali will be twice as old as Nitesh. What are their present ages?

Answer 1

Hint: First of all, we will assume Ali’s age as any variable such as, x. Then using that we will find the age of Nitesh which is 5 times the age of Ali’s. Then we will find the expression of their ages after 9 years and considering the age of Ali as twice that of Nitesh. Then comparing the expressions, we will find the value of the variable and then from that we will find the value of present ages of both.

Complete step-by-step answer:
In question we are given that Ali’s age is 5 times that of Nitesh, so first of all we will assume Ali’s age as $x$ . As Ali’s age is $x$, Nitesh’s age will be $5x$, which can be written mathematically as,
Ali’s present age $=x$ ………………..(i)
Nitesh present age $=5x$ ………………...(ii)
Now, for ages of both after 9 years we have to add 9 in both expressions, so the expressions will become,
Ali’s age after 9 years $=x+9$ ……………(iii)
Nitesh’s age $=5x+9$ ………………(iv)
Now, it is given in question that Ali’s age after 9 years is twice the age of Nitesh after 9 years, which can be given as,
$2\left( x+9 \right)=5x+9$
$\Rightarrow 2x+18=5x+9$
$\Rightarrow 18-9=5x-2x$
$\Rightarrow 9=3x$
$\Rightarrow x=\dfrac{9}{3}=3$
Now, on substituting these values in expression (i) and (ii) we will get,
Ali’s present age $=x=3years$
Nitesh’s present age $=5\left( 3 \right)=15years$
Hence, the present age of Ali and Nitesh is 5 years and 15 years respectively.

Note: In question it is given that after 9 years Ali will be twice as old as Nitesh, which means we have to consider the age of Ali as twice the age of Nitesh which we did in solution. But students might interpret the sentence wrong and they might consider the age of Nitesh as twice the age of Ali, due to which our expression becomes, $x+9=2\left( 5x+9 \right)$. Now, on solving the expression the value of x will be, $-1$ and age cannot be negative so it is wrong and the whole solution will be wrong. So, students must understand the question carefully and solve accordingly.