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%

Hint:

To calculate the required percentage profit, first calculate the total selling price based on desired total profit, then find the required price for the second item.

Answer 1

The Correct Option is D

Let the cost price of each bicycle be Rs. 3500.
The first bicycle is sold at a 5% profit: \[ \text{Selling Price of 1st bicycle} = 3500 + (5% \times 3500) = 3500 + 175 = 3675 \] Now, the total desired profit on both bicycles is 20%, so the total selling price for both must be: \[ \text{Total Selling Price} = 3500 \times 2 + 20% \times (3500 \times 2) = 7000 + 1400 = 8400 \] Thus, the selling price of the second bicycle should be: \[ \text{Selling Price of 2nd bicycle} = 8400 - 3675 = 4725 \] The profit on the second bicycle is: \[ \text{Profit} = 4725 - 3500 = 1225 \] The percentage profit on the second bicycle is: \[ \frac{1225}{3500} \times 100 = 35% \] Hence, the second bicycle should be sold at a 35% profit.

Answer 2

Naresh wants an overall profit of 20 percent on two bicycles, each bought for Rs. 3500, given the first is sold at a 5 percent profit. We need the profit percentage on the second bicycle. We can test each option by checking whether it gives the required overall 20 percent profit.

1. 15%: Selling price of the first bicycle is \( 3500 \times 1.05=3675 \). Selling price of the second at 15 percent profit is \( 3500 \times 1.15=4025 \). Total is \( 3675+4025=7700 \), an overall profit of \( \frac{7700-7000}{7000} \times 100=10\% \), not 20 percent.
2. 10%: Selling price of the second bicycle at 10 percent profit is \( 3500 \times 1.10=3850 \). Total is \( 3675+3850=7525 \), an overall profit of \( \frac{7525-7000}{7000} \times 100=7.5\% \), not 20 percent.
3. 25%: Selling price of the second bicycle at 25 percent profit is \( 3500 \times 1.25=4375 \). Total is \( 3675+4375=8050 \), an overall profit of \( \frac{8050-7000}{7000} \times 100=15\% \), not 20 percent.
4. 35%: Selling price of the second bicycle at 35 percent profit is \( 3500 \times 1.35=4725 \). Total is \( 3675+4725=8400 \), an overall profit of \( \frac{8400-7000}{7000} \times 100=20\% \), matching exactly.

Only a 35 percent profit on the second bicycle brings the combined selling price to Rs. 8400, exactly a 20 percent overall profit on the total cost price of Rs. 7000.

Therefore, the correct answer is 35%.

Answer 3

Since both bicycles cost the same, Rs. 3500 each, the overall percentage profit on the two together is simply the plain average of the two individual profit percentages. With the first bicycle sold at a 5 percent profit and an overall target of 20 percent, we can test each option by checking whether its average with 5 percent comes to 20 percent.

1. 15%: The average of 5 percent and 15 percent is \( \tfrac{5+15}{2}=10\% \), not the required 20 percent.
2. 10%: The average of 5 percent and 10 percent is \( \tfrac{5+10}{2}=7.5\% \), well short of 20 percent.
3. 25%: The average of 5 percent and 25 percent is \( \tfrac{5+25}{2}=15\% \), still short of 20 percent.
4. 35%: The average of 5 percent and 35 percent is \( \tfrac{5+35}{2}=20\% \), matching the required overall profit exactly.

Because the two bicycles have equal cost prices, their combined profit percentage is just the average of the two individual percentages, and only 35 percent on the second bicycle averages out to the required 20 percent.

Therefore, the correct answer is 35%.