A man bought 72 toys for Rs.
x. Out of them, 18 toys are damaged and 54 are undamaged. One-third of the damaged toys are sold at 25% loss and the remaining damaged toys are sold at 20% loss. The undamaged toys are sold at 10% profit. If total selling price is Rs. (x + 90), find the cost price of each toy.

ATQ, Cost price of one toy = x/72 Damaged toys = 18 1/3 of 18 = 6 toys sold at 25% loss ⇒ factor = 75/100 Remaining damaged toys = 12 sold at 20% loss ⇒ factor = 80/100 Undamaged toys = 54 sold at 10% profit ⇒ factor = 110/100 So, 6 × (x/72) × (75/100) + 12 × (x/72) × (80/100) + 54 × (x/72) × (110/100) = x + 90 Or, 6 × (x/72) × (3/4) + 12 × (x/72) × (4/5) + 54 × (x/72) × (11/10) = x + 90 Or, x/16 + 2x/15 + 33x/40 = x + 90 Or, 15x/240 + 32x/240 + 198x/240 = x + 90 Or, 245x/240 = x + 90 Or, 49x/48 = x + 90 Or, 49x = 48x + 4320 Or, x = 4320 Cost price of one toy = x/72 = 4320/72 = Rs. 60