The present age of Salil's mother is three times Salil's present age. After 5 years, their ages will add up to 70 years. Find their present ages.

Question

Homi · Accepted Answer

Understand the Question

Let Salil's present age be $x$ years. Since his mother's age is three times his age, her present age is $3x$ years.
After $5$ years, both individuals grow older by $5$ years, making their ages $(x + 5)$ and $(3x + 5)$ .
Setting the sum of their future ages equal to $70$ gives a linear equation in one variable, which we solve to find their present ages.

Step 1 · Define Ages and Form the Equation

Let Salil's present age be $x$ years. Mother's present age $= 3x$ years.

After $5$ years:

Given that the sum of their ages after $5$ years is $70$ : $(x + 5) + (3x + 5) = 70$

Step 2 · Solve for $x$

$4x + 10 = 70$

\begin{aligned} 4x &= 70 - 10 \\ 4x &= 60 \end{aligned}

$x = \dfrac{60}{4} = 15$

Step 3 · Calculate Present Ages

Substitute $x = 15$ into the expressions for their present ages:

Answer

Salil's present age is $15$ years and his mother's present age is $45$ years.

Common Mistakes

Adding $5$ to Only One Person: Forgetting that both people age by $5$ years, mistakenly writing $x + 3x + 5 = 70$ instead of $(x + 5) + (3x + 5) = 70$ .
Stopping at $x$ : Finding $x = 15$ and forgetting to evaluate the mother's age ( $3x = 45\text{ years}$ ).

Question 3