CAT 2025Slot 2QAQuestion & Solution
Question
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
Options
2:1
1:2
5:8
8:5
Solution
1. Concept Used
- Topic: Percentage — Sequential distribution of a total amount among multiple people
- Formula: $$\text{Share} = \text{Percentage} \times \text{Relevant Base Amount}$$
2. Calculation
Let the total amount be $100$ units (a clean base that simplifies all percentage calculations).
Pinu's Share: Pinu receives $20%$ of the total amount. $$\text{Pinu} = 20% \times 100 = 20 \text{ units}$$ Amount remaining after Pinu's share: $$100 - 20 = 80 \text{ units}$$
Meena's Share: Meena receives $40%$ of the remaining $80$ units (not the total — this is a key distinction). $$\text{Meena} = 40% \times 80 = 0.40 \times 80 = 32 \text{ units}$$ Amount remaining for Rinu and Seema together: $$80 - 32 = 48 \text{ units}$$
Seema's Share: Seema receives $20%$ less than Pinu. Since Pinu received $20$ units: $$\text{Seema} = 20 - (20% \times 20) = 20 - 4 = 16 \text{ units}$$
Rinu's Share: From the $48$ units left for Rinu and Seema combined, subtracting Seema's $16$ units gives: $$\text{Rinu} = 48 - 16 = 32 \text{ units}$$
Required Ratio — Pinu : Rinu: $$\text{Pinu} : \text{Rinu} = 20 : 32$$ 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 $\mathbf{5 : 8}$.