GATE 2022 PH – Question 7
P invests 5000 rupees per month for 6 months; Q invests x rupees per month for 8 months. Profit is proportional to total investment that year. Q receives 4/9 of the total profit. Find x.
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Correct answer: (B) 3000
Explanation
Profit is shared in proportion to the **total investment** (amount × months).
- **P:** $5000\times6=30\,000$ rupee-months.
- **Q:** $x\times8=8x$ rupee-months.
Q receives $\tfrac49$ of the profit, so P receives $\tfrac59$. The ratio of the investments equals the ratio of the profits:
$$\frac{8x}{30\,000}=\frac{4/9}{5/9}=\frac45\;\Rightarrow\;8x=24\,000\;\Rightarrow\;x=\mathbf{3000}.$$
(Check: $8\times3000=24\,000$ and $24\,000/54\,000=4/9$ ✓.)