Question

If Rajesh’s age were to be the present age of Shivani, their age ratio would be \(3:2\). Then what would be their present age ratio?

• A. 2:3
• B. 3:2
• C. 4:2
• D. 1:2

Answer 1

The Correct Option is A

To solve the problem, we need to determine the present age ratio of Rajesh to Shivani. The given condition is that if Rajesh’s age were to be the present age of Shivani, their age ratio would be \(3:2\). Let's assume:

Let R be the present age of Rajesh and S be the present age of Shivani.

According to the problem, if Rajesh’s age becomes Shivani’s current age (i.e., if Rajesh were as old as Shivani is now), then the ratio becomes \(3:2\). This implies:

\( \frac{S}{R} = \frac{3}{2} \)

From this equation, we can infer that Shivani is older than Rajesh. Let us solve for the present age ratio \( \frac{R}{S} \) by inverting the given ratio:

\( \frac{R}{S} = \frac{2}{3} \)

Thus, their present age ratio is \(2:3\).

Therefore, the correct answer is 2:3.

Answer 2

Let \( R \) be Rajesh's current age and \( S \) be Shivani's current age.

We are given that if Rajesh's age were Shivani's current age, the ratio would be \( 3:2 \). This can be expressed as:

\(\frac{S}{R} = \frac{3}{2}\)     (1)

From this equation, we can express \( R \) in terms of \( S \):

\(R = \frac{2}{3}S\)     (2)

The present age ratio is \( R : S \). Substituting the expression for \( R \) from Equation (2):

\(\frac{2}{3}S : S\)        (3)

Multiplying both sides by 3 to simplify:

\(2S : 3S\)      (4)

Assuming \( S \) is not zero, we can divide both sides by \( S \):

\(2 : 3\)       (5)

Therefore, their present age ratio is \( 2 : 3 \).