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

Step 1: The total cost of both bicycles is \( 3500 \times 2=7000 \). A 20 percent overall profit means the total profit needed is \( 0.20 \times 7000=1400 \).

Step 2: The profit earned on the first bicycle, sold at 5 percent, is \( 0.05 \times 3500=175 \).

Step 3: The profit still needed from the second bicycle is \( 1400-175=1225 \).

Step 4: This profit as a percentage of the second bicycle's cost price is \( \frac{1225}{3500} \times 100=35\% \).
\[ \boxed{35\%} \]

Answer 2

Express each selling price as a multiple of the common cost price: the first bicycle sells at a multiplier of \( 1.05 \) (its 5 percent profit), and the combined target requires the two multipliers to average to \( 1.20 \) (the 20 percent overall profit), so their sum must be \( 2 \times 1.20=2.40 \). We can test each option by checking whether \( 1.05 \) plus its multiplier adds up to 2.40.

1. 15%: Multiplier \( 1.15 \); sum with 1.05 is \( 1.05+1.15=2.20 \), not 2.40.
2. 10%: Multiplier \( 1.10 \); sum with 1.05 is \( 1.05+1.10=2.15 \), not 2.40.
3. 25%: Multiplier \( 1.25 \); sum with 1.05 is \( 1.05+1.25=2.30 \), not 2.40.
4. 35%: Multiplier \( 1.35 \); sum with 1.05 is \( 1.05+1.35=2.40 \), matching exactly.

Since the two selling-price multipliers must add up to \( 2.40 \) for an overall 20 percent profit, and the first bicycle already contributes \( 1.05 \), the second bicycle needs a multiplier of \( 1.35 \), a 35 percent profit.

Therefore, the correct answer is 35%.