Question

If Fatima sells 60 identical toys at a 40% discount on the printed price, then she makes 20% profit. Ten of these toys are destroyed in fire. While selling the rest, how much discount should be given on the printed price so that she can make the same amount of profit?

• A. 30%
• B. 25%
• C. 24%
• D. 28%

Answer 1

The Correct Option is D

Step 1: Printed price and discount

Let the printed price of each toy be \( p \). If a 40% discount is given: \[ \text{Selling price} = 0.6 \times (60p) = 36p \]

Step 2: Profit target

To make a 20% profit, the selling price should be: \[ \text{Selling price} = 1.2 \times \text{Total cost price} \] From the earlier selling price: \[ \text{Cost price total} = \frac{36p}{1.2} = 30p \]

Step 3: Fire accident effect

Ten toys are destroyed in the fire. The remaining toys are sold in such a way that the total profit is the same as in the original (conditional) case.

Step 4: Profit on remaining toys

Profit per toy in the earlier case: \[ \text{Profit per toy} = 36p - 30p = 6p \] Thus, for the remaining toys, total profit = \( 6p \) per toy × number of toys left.

Step 5: Required discount

The total selling price of the remaining toys is \( 36p \). The printed price total for the remaining toys is \( 50p \). Hence, discount amount: \[ \text{Discount} = 50p - 36p = 14p \]

Step 6: Discount percentage

\[ \text{Discount\%} = \frac{14p}{50p} \times 100 = 28\% \]

Final Answer:

\[ \boxed{\text{28\% discount}} \]