Question

Naresh bought a bicycle each for his two sons, each bicycle priced at Rs. 3500. If the first bicycle is sold at a profit of 5%, the how much should the other bicycle be sold for, to gain a total of 20% on both?

• A. 15%
• B. 10%
• C. 25%
• D. 35%

Answer 1

The Correct Option is D

The correct option is (D): 35%.

Answer 2

Naresh bought two bicycles, each costing Rs. 3500, so the total cost is Rs. 7000. The first is sold at a 5% profit. We need the profit percentage on the second bicycle so that the overall profit across both bicycles is 20%. Let's check each option by computing the total profit it would produce.

1. Option (A): 15%: Selling the second bicycle at 15% profit gives Rs. 3500 x 1.15 = Rs. 4025. Total revenue = Rs. 3675 (first bicycle) + Rs. 4025 = Rs. 7700, a profit of Rs. 700 on Rs. 7000, which is only 10%, not 20%.
2. Option (B): 10%: At 10% profit, the second bicycle sells for Rs. 3850. Total revenue = Rs. 3675 + Rs. 3850 = Rs. 7525, a profit of Rs. 525, which is 7.5%, far short of 20%.
3. Option (C): 25%: At 25% profit, the second bicycle sells for Rs. 4375. Total revenue = Rs. 3675 + Rs. 4375 = Rs. 8050, a profit of Rs. 1050, which is 15%, still short of 20%.
4. Option (D): 35%: At 35% profit, the second bicycle sells for Rs. 4725. Total revenue = Rs. 3675 + Rs. 4725 = Rs. 8400, a profit of Rs. 1400 on Rs. 7000, which is exactly 20%.

Only a 35% profit on the second bicycle brings the overall profit on both bicycles to the required 20%.

Therefore, the correct answer is 35%.

Answer 3

Naresh's total cost for both bicycles is \( 3500+3500=7000 \). For an overall profit of 20%, the total profit needed is \[ 0.20\times7000=1400. \] The first bicycle, sold at 5% profit, earns a profit of \[ 0.05\times3500=175. \] The profit still needed from the second bicycle is therefore \[ 1400-175=1225, \] and as a percentage of its own cost price of 3500, this is \[ \frac{1225}{3500}\times100=35\%. \] Check each option against this required profit of Rs. 1225 on the second bicycle.

1. Option (A): 15%: A 15% profit on the second bicycle gives \( 0.15\times3500=525 \), far short of the Rs. 1225 profit still needed to reach the overall 20% target.
2. Option (B): 10%: A 10% profit gives \( 0.10\times3500=350 \), even further from the required Rs. 1225.
3. Option (C): 25%: A 25% profit gives \( 0.25\times3500=875 \), closer but still Rs. 350 short of the Rs. 1225 needed.
4. Option (D): 35%: A 35% profit gives \( 0.35\times3500=1225 \), matching exactly the profit still required from the second bicycle after accounting for the first.

Subtracting the first bicycle's actual profit from the total profit required for a 20% overall gain shows the second bicycle must earn Rs. 1225, which corresponds to a 35% profit.

Therefore, the correct answer is 35%.