Q.7 In a partnership business the monthly investment by three friends for the first
six months is in the ratio 3: 4: 5. After six months, they had to increase their
monthly investments by 10%, 15% and 20%, respectively, of their initial
monthly investment. The new investment ratio was kept constant for the next
six months.
What is the ratio of their shares in the total profit (in the same order) at the end
of the year such that the share is proportional to their individual total investment
over the year?
(A) 22 : 23 : 24
(B) 22 : 33 : 50
(C) 33 : 46 : 60
(D) 63 : 86 : 110
Step-by-Step Solution
Let the initial monthly investments of the three friends (A, B, C) be 3x, 4x, and 5x respectively for the first 6 months.
Total Investment Calculation
- First 6 months: A: 3x × 6 = 18x, B: 4x × 6 = 24x, C: 5x × 6 = 30x
After 6 months, new monthly investments become:
- A: 3x × 1.10 = 3.3x
- B: 4x × 1.15 = 4.6x
- C: 5x × 1.20 = 6x
Maintained for the next 6 months:
- A: 3.3x × 6 = 19.8x
- B: 4.6x × 6 = 27.6x
- C: 6x × 6 = 36x
Profit Share Ratio
Total investments:
- A: 18x + 19.8x = 37.8x
- B: 24x + 27.6x = 51.6x
- C: 30x + 36x = 66x
Ratio: 37.8x : 51.6x : 66x
Multiply by 10 to eliminate decimals: 378 : 516 : 660
Divide by 6: 63 : 86 : 110
Option Analysis
| Option | Ratio | Status | Reason |
|---|---|---|---|
| (A) | 22:23:24 | Incorrect | Too close ratios ignore investment differences |
| (B) | 22:33:50 | Incorrect | Understates A’s and B’s shares relative to increases |
| (C) | 33:46:60 | Incorrect | Fails to account full percentage hikes precisely |
| (D) | 63:86:110 | Correct | Matches exact total investment ratio |
Why This Ratio Matters
Profit proportionality to total investment (amount × time) ensures fair shares in partnerships with varying contributions, a key concept for competitive exams.
Common Mistakes in Options
- 22:23:24 assumes constant ratios without increases
- 33:46:60 mishandles percentages
- Always compute both periods separately
