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?
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?
Updated On: Jul 30, 2025
- 30%
- 25%
- 24%
- 28%
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
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:
\[ \boxed{\text{28\% discount}} \]
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