CAT 2025

Slot 2

QA

Question & SolutionQues & Sol

A certain amount of money was divided among Pinu, Meena, Rinu and Seema. Pinu received 20% of the total amount and Meena received 40% of the remaining amount. If Seema received 20% less than Pinu, the ratio of the amounts received by Pinu and Rinu is

1. Concept Used

• Topic: Percentage — Sequential distribution of a total amount among multiple people
• Formula: $$\text{Individual Share} = \text{Given Percentage} \times \text{Relevant Base Amount}$$

2. Calculation

Let the total amount be $T = 100$ units. Choosing 100 as the base eliminates decimal clutter and makes every percentage calculation clean and direct.

Step 1 — Pinu's Share: Pinu receives $20%$ of the total amount, so: $\text{Pinu} = 20% \times 100 = 20 \text{ units}$ After Pinu's share, the remaining amount is: $100 - 20 = 80 \text{ units}$

Step 2 — Meena's Share (critical distinction): Meena receives $40%$ of the remaining amount, NOT of the total. This is a classic trap — always track the base carefully. $\text{Meena} = 40% \times 80 = 0.40 \times 80 = 32 \text{ units}$ Amount left for Rinu and Seema together: $80 - 32 = 48 \text{ units}$

Step 3 — Seema's Share: Seema receives $20%$ less than Pinu. Since Pinu received $20$ units: $\text{Seema} = 20 - (20 percent of 20) = 20 - 4 = 16 \text{ units}$

Step 4 — Rinu's Share: The remaining $48$ units are shared between Rinu and Seema. Subtracting Seema's portion: $\text{Rinu} = 48 - 16 = 32 \text{ units}$

Step 5 — Computing the Required Ratio: Now we have Pinu $= 20$ units and Rinu $= 32$ units. The ratio is: $\text{Pinu} : \text{Rinu} = 20 : 32$ Dividing both terms by their GCD, which is $4$: $= \frac{20}{4} : \frac{32}{4} = 5 : 8$

3. Solution

Answer = Option C (5:8) ✅

The ratio of the amounts received by Pinu and Rinu is $\mathbf{5 : 8}$.