Q.7 P invested ₹ 5000 per month for 6 months of a year and Q invested ₹ 𝑥 per
month for 8 months of the year in a partnership business. The profit is shared in
proportion to the total investment made in that year.
If at the end of that investment year, Q receives 4/9 of the total profit, what is the
value of 𝑥 (in ₹)?
(A) 2500
(B) 3000
(C) 4687
(D) 8437
P’s total investment: ₹5000 × 6 = ₹30,000. Q receives 4/9 of the total profit, meaning Q’s investment share is also 4/9 of total investment since profit shares in proportion to total investment.
Let Q’s monthly investment be x, so Q’s total is 8x; set up the ratio 8x / (30,000 + 8x) = 4/9 and solve for x = 3000.
Step-by-Step Solution
- Cross-multiply:
9(8x) = 4(30,000 + 8x) - This yields:
72x = 120,000 + 32x - Subtract 32x from both sides:
40x = 120,000 - So
x = 3000 - Total investment becomes ₹54,000, with Q’s ₹24,000 exactly 4/9 (
24/54 = 4/9)
Option Analysis
| Option | x (₹) | Q Total (₹) | Total Inv. (₹) | Q Share | Matches 4/9? |
|---|---|---|---|---|---|
| (A) | 2500 | 20,000 | 50,000 | 2/5 | No |
| (B) | 3000 | 24,000 | 54,000 | 4/9 | ✓ Correct |
| (C) | 4687 | 37,496 | 67,496 | ~5/9 | No |
| (D) | 8437 | 67,496 | 97,496 | ~11/17 | No |
Partnership profit sharing based on total investment is a common quantitative aptitude topic in competitive exams like IIT JAM, SSC, and banking tests. In this problem, P invests ₹5000 per month for 6 months (total ₹30,000), while Q invests x per month for 8 months (total 8x). Profits divide proportionally, and Q gets 4/9 of total profit.
Core Calculation
Set ratio: 8x/(30000+8x)=4/9. Solve: 72x=120000+32x, 40x=120000, x=3000. Verify: Q’s ₹24,000 / ₹54,000 = 4/9.
Exam Tips
- Practice similar partnership profit sharing investment ratio problems by varying months/capital
- Always compute totals first, then ratio equation
- Correct answer: (B) 3000
