EXAMPLE PROBLEMS ON PROFIT AND LOSS
Profit (or) gain = Selling price - Cost price
Loss = Cost price - Selling price
Profit % = (Profit / Cost price) ⋅ 100
Loss % = (Loss / Cost price) ⋅ 100
Cost price = [100 / (100 - loss%)] ⋅ Selling price
Cost price = [100 / (100 + profit%)] ⋅ Selling price
Selling price = [(100 + profit%)/100] ⋅ Cost price
Selling price = [(100 - loss%)/100] ⋅ Cost price
Example 1 :
A shop bought 80 laptops at $4000 each. It then sold 50 of them at a 20% profit in the first month. In the second month, the remaining laptops were sold at 75% of the first month's selling price. How much profit was made altogether ?
Solution :
Selling price of each laptop sold in the first month = 120% of 4000
= 1.2(4000)
= 4800
Cost price of 50 laptops at 4000 each :
= 50(4000)
= 200000
Selling price of 50 laptops at 4800 each :
= 50(4800)
= 240000
Profit in the first month = 240000 - 200000
= 40000
Remaining laptops = 80 - 50 = 30
Selling price of each laptop in the second month = 75% of selling price of first month
= 75% of 4800
= 3600
Cost price of 30 laptops = 30(4000)
= 120000
Selling price of 30 laptops = 30(3600)
= 108000
Loss in the second month = 120000 - 108000
= 12000
Profit earned altogether = 40000 - 12000
= 28000
Example 2 :
A product was marked at 20% above the cost price. It was eventually sold at 80% of the selling price. The loss was $40. What was the cost price of the product ?
Solution :
Let x be the cost price
Marked price = 120% of x
Selling price = 80% of 120% of x
= 0.8 (1.2x)
= 0.96x
Loss = Cost price - Selling price
x - 0.96x = 40
0.04x = 40
x = 40/0.04
x = 1000
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