GATE 2022 BT – Question 7
P invests ₹5000 per month for 6 months and Q invests ₹x per month for 8 months. Profit follows total annual investment. Q receives $4/9$ of the profit. What is 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 $\dfrac49$ of the profit, so
$$\frac{8x}{30\,000+8x}=\frac49 .$$
**Cross-multiply:**
$$9(8x)=4(30\,000+8x)\;\Rightarrow\;72x=120\,000+32x\;\Rightarrow\;40x=120\,000\;\Rightarrow\;x=\mathbf{3000}.$$
Check: $8(3000)=24\,000$ and $24\,000/54\,000=4/9$ ✓.