What is the overall percentage gain or loss of the company?

Question

A company divides its total investment of Rs. 12,00,000 among three projects A, B and C in the ratio 2 : 3 : 5. After one year:

Project A gives a return of 10% profit

Project B gives a return of 20% profit

Project C incurs a 10% loss

What is the overall percentage gain or loss of the company?

1. A. 3% loss
2. B. 3% profit (Correct answer)
3. C. 3.6% profit
4. D. 3.6% loss

Correct Answer

Option B — 3% profit

Detailed Solution & Explanation

The correct answer is 3% profit.

Key Points

• Step 1 — divide the investment in the ratio 2 : 3 : 5. Total parts $= 10$, so one part $= \dfrac{12{,}00{,}000}{10} = 1{,}20{,}000$.
  • Project A $= 2 \times 1{,}20{,}000 = 2{,}40{,}000$
  • Project B $= 3 \times 1{,}20{,}000 = 3{,}60{,}000$
  • Project C $= 5 \times 1{,}20{,}000 = 6{,}00{,}000$
• Step 2 — compute each return.
  • A: $+10\%$ of $2{,}40{,}000 = +24{,}000$
  • B: $+20\%$ of $3{,}60{,}000 = +72{,}000$
  • C: $-10\%$ of $6{,}00{,}000 = -60{,}000$
• Step 3 — net the result.
  • $24{,}000 + 72{,}000 - 60{,}000 = +36{,}000$
• Step 4 — express as a percentage of total investment.
  • $\frac{36{,}000}{12{,}00{,}000} \times 100 = \mathbf{3\% \text{ profit}}$

Shortcut Trick

• Work in ratio parts and skip the rupee figures entirely. Taking the parts as 2, 3 and 5:
  • $2 \times 0.10 + 3 \times 0.20 + 5 \times (-0.10) = 0.2 + 0.6 - 0.5 = 0.3$
• Divide by the 10 total parts: $\frac{0.3}{10} = 0.03 = \mathbf{3\%}$ profit. This is the weighted average of the three returns and takes a single line.

Additional Information

• The weighted-average formula for combined returns:
  • $\text{Net }\% = \frac{\sum (\text{weight} \times \text{return}\%)}{\sum \text{weights}}$
• Sanity check on the sign: the two gains total $+96{,}000$ against a loss of $60{,}000$, so the overall result must be a profit. That alone eliminates both "loss" options before any division is performed.
• Distractor check: 3.6% arises from dividing the net gain by the wrong base — for instance by $10{,}00{,}000$ instead of $12{,}00{,}000$. The percentage must always be taken on the total investment.