Problem 1 :
The product is marked at 20% above the cost price. It is then sold at 90% of the selling price. The profit is $120. What is the cost price of this product.
Let x be the the cost price.
120% of x = Marked price
Selling price = 90% of marked price
= 90% of (120% of x)
Profit = $120 ---(1)
Profit = Cost price - Selling price
= x - 1.08x
= x(1 - 1.08)
Profit = 0.08x ---(2)
(1) = (2)
0.08x = 120
x = 120/0.08
x = 1500
So, the cost price is 1500.
Problem 2 :
A shop purchased some shoes at $65 per pair. It then sold them at $74 per pair. The shopkeeper calculated that the profit earned was $440 when there were 5 pairs of shoes left. How many pairs of shoes did the shop purchase initially ?
Let x be the number of pair of shoes in the shop.
Pair of shoes left = 5
Cost price of pair of shoes going to be sold = 65x
Selling price of pair of shoes has been sold = 74(x - 5)
Profit = 440
Profit = Selling price - Cost price
74(x - 5) - 65x = 440
74x - 370 - 65x = 440
9x = 440 + 370
9x = 810
x = 810/9
x = 90
So, the shop purchased 90 pairs of shoes initially.
Problem 3 :
The selling price of a sofa set is $12000. It is later sold at $6500 at an exhibition. The profit made is 30%. What is the percentage of profit if the profit is $5000 ?
Selling price of a sofa = 12000
By selling the sofa at the cost of $6500, it made a profit 30%.
Let x be the cost price of sofa.
130% of x = 6500
1.30x = 6500
x = 6500/1.30
x = 5000
Cost price of sofa is 5000.
Profit % = (Profit / cost price) ⋅ 100
= (5000/5000) ⋅ 100
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