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?

Correct Option: D

Let the printed price (marked price) of each toy be M, and the cost price of each toy be C.
The total cost price for 60 toys is 60C.

Initially, she sells 60 toys at a 40% discount on the printed price:
Selling Price (SP) per toy = 0.6M
Total SP for 60 toys = 60 * 0.6M = 36M

She makes a 20% profit on the total cost price:
Total SP = 1.2 * (Total CP)
36M = 1.2 * 60C
36M = 72C
M = 2C

So, the printed price (M) is twice the cost price (C).
The absolute profit amount made initially is:
Profit = Total SP - Total CP = 36M - 60C = 36(2C) - 60C = 72C - 60C = 12C.

Ten toys are destroyed in a fire, so she has 50 toys left to sell.
To make the same profit amount (12C), the new total selling price (New SP) for the remaining 50 toys must be:
New SP = Total CP + Profit = 60C + 12C = 72C

Let the new discount percentage offered on the printed price of the remaining toys be d.
Selling price per toy = M * (1 - d) = 2C * (1 - d)
New SP for 50 toys = 50 * 2C * (1 - d) = 100C * (1 - d)

Equating the two expressions for New SP:
100C * (1 - d) = 72C
1 - d = 0.72
d = 0.28, which is 28%

Therefore, she should give a 28% discount on the printed price of the remaining toys to make the same amount of profit.