Rohit spends 40\% of his monthly income on rent, and then spends $\frac{1}{3}$ of the remaining income on groceries. He invests the rest of his income in three different schemes A, B, and C in the ratio 2 : 3 : 5 respectively. The difference between the amounts invested in scheme B and scheme C is Rs 4000.

**Quantity I:** Find the difference between Rohit's monthly income and the amount invested in scheme C.

**Quantity II:** Rs 60000

Compare Quantity I and Quantity II.

Question

Rohit spends 40\% of his monthly income on rent, and then spends $\frac{1}{3}$ of the remaining income on groceries. He invests the rest of his income in three different schemes A, B, and C in the ratio 2 : 3 : 5 respectively. The difference between the amounts invested in scheme B and scheme C is Rs 4000.

**Quantity I:** Find the difference between Rohit's monthly income and the amount invested in scheme C.

**Quantity II:** Rs 60000

Compare Quantity I and Quantity II.

Accepted Answer

**Solution:**

1. Let Rohit's monthly income be $x$.

2. He spends 40\% on rent, so amount spent on rent = $0.4x$.

3. Remaining income after rent = $x - 0.4x = 0.6x$.

4. He spends $\frac{1}{3}$ of the remaining on groceries:
   $$
   \text{Groceries} = \frac{1}{3} \times 0.6x = 0.2x
   $$

5. Remaining income after groceries = $0.6x - 0.2x = 0.4x$.

6. This remaining $0.4x$ is invested in schemes A, B, and C in ratio 2 : 3 : 5.

7. Total parts = $2 + 3 + 5 = 10$.

8. Amount invested in scheme B = $\frac{3}{10} \times 0.4x = 0.12x$.

9. Amount invested in scheme C = $\frac{5}{10} \times 0.4x = 0.2x$.

10. Given difference between amount invested in B and C is Rs 4000:
    $$
    0.2x - 0.12x = 4000 \
    0.08x = 4000 \
    x = \frac{4000}{0.08} = 50000
    $$

11. Rohit's monthly income $x = 50000$.

12. Amount invested in scheme C = $0.2 \times 50000 = 10000$.

13. Difference between monthly income and amount invested in scheme C:
    $$
    50000 - 10000 = 40000
    $$

14. Quantity I = 40000

15. Quantity II = 60000

16. Compare Quantity I and Quantity II:
    $$
    40000 < 60000
    $$

**Answer:** (b) Quantity I < Quantity II

**Note:** The correct answer is option (b), Quantity I is less than Quantity II.

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