An antique dealer sold three items, A, B, and C, with their selling prices in the ratio 4 : 5 : 6. He suffered a loss of 10% on i…

Question

An antique dealer sold three items, A, B, and C, with their selling prices in the ratio 4 : 5 : 6. He suffered a loss of 10% on item A, made a profit of 50% on item B, and broke even (no profit, no loss) on item C. What was his approximate percentage gain or loss in the overall deal?

1. A. loss of 8.88%
2. B. profit of 8.88% (Correct answer)
3. C. profit of 10.88%
4. D. loss of 10.88%

Correct Answer

Option B — profit of 8.88%

Detailed Solution & Explanation

The correct answer is profit of 8.88%.

Key Points

• The selling prices are in the ratio 4 : 5 : 6, so work back to each cost price:
  • A sold at a 10% loss: CP = 4 ÷ 0.9 = 4.444
  • B sold at a 50% profit: CP = 5 ÷ 1.5 = 3.333
  • C broke even: CP = 6
• Total CP = 4.444 + 3.333 + 6 = 13.778; total SP = 4 + 5 + 6 = 15.
• Overall gain = (15 − 13.778) ÷ 13.778 × 100 ≈ 8.88% profit.

Additional Information

• The ratio is given for selling prices, so the cost prices must be derived by dividing — multiplying instead is the standard error, and it reverses the sign of the answer.
• Divide by (1 + profit%) or (1 − loss%) to move from SP to CP; multiply to go the other way.
• A quick check on direction: B's 50% profit is far larger than A's 10% loss, and C is neutral, so an overall profit is expected — which eliminates both "loss" options immediately.

प्रश्न (हिन्दी में)

एक एंटिक डीलर ने तीन वस्तुएं A, B और C बेचीं, जिनके विक्रय मूल्य का अनुपात 4 : 5 : 6 था। उसे वस्तु A पर 10% की हानि हुई, वस्तु B पर 50% का लाभ हुआ, तथा वस्तु C पर बराबर रहा (न लाभ, न हानि)। कुल सौदे में उसका अनुमानित लाभ या हानि प्रतिशत क्या था?

1. A. 8.88% की हानि
2. B. 8.88% का लाभ
3. C. 10.88% का लाभ
4. D. 10.88% की हानि