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CAT 2025 Slot 2 QA Question & Solution

ArithmeticMedium

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

Let the total amount be $100$ units (taking $100$ makes percentage calculations easier).

  • Pinu's Share: Pinu receives $20%$ of the total. $$Pinu = 20% \times 100 = 20 \text{ units}$$ The amount left after giving Pinu his share is: $$100 - 20 = 80 \text{ units}$$

  • Meena's Share: Meena receives $40%$ of this remaining amount ($80$). $$Meena = 40% \times 80 = 32 \text{ units}$$ Now, the amount left for Rinu and Seema together is: $$80 - 32 = 48 \text{ units}$$

  • Seema's Share: Seema receives $20%$ less than Pinu. Since Pinu gets $20$ units: $$Seema = 20 - (20% \times 20) = 20 - 4 = 16 \text{ units}$$

  • Rinu's Share: Out of the $48$ units left for Rinu and Seema, Seema’s share is $16$ units. Therefore, Rinu gets: $$Rinu = 48 - 16 = 32 \text{ units}$$

Conclusion: Pinu receives $20$ units, and Rinu gets $32$ units. The required ratio of Pinu : Rinu is: $$20 : 32$$ Dividing both terms by $4$: $$\mathbf{5 : 8}$$