A shopkeeper has some toys. He sells two-third of the toys at a profit of 35% and the remaining toys at 10% loss. What is his overall perecentage of profit?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 20%.
A shopkeeper has some toys. He sells two-thirds of the toys at a profit of 35% and the remaining toys at a 10% loss.
Selling Price = Cost Price - Cost Price × Loss%
Selling Price = Cost Price + Cost Price × Gain%
Profit% = [(Selling Price - Cost Price)/Cost Price] × 100
Let there be 3x the number of toys at the shop.
Number of toys sold at 35% profit = 3x × 2/3 = 2x
Number of toys sold at 10% loss = 3x - 2x = x
Let the cost price of each toy be y.
The total cost price of all toys = 3xy
Selling price of 2x number of toys = 2x(y + y × 35%) = 2x(y + 0.35y) = 2x × 1.35y = 2.7xy
Selling price of x number of toys = x(y - y × 10%) = x(y + 0.1y) = x × 0.9y = 0.9xy
Overall profi% = [{(2.7xy + 0.9xy) - 3xy}/xy] × 100% = 0.6(100)/3 = 20%