Find the Selling Price if we Want to Make a Given Profit or Loss :
In this section, we will see how to solve problems with the concept of 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 fruit seller sells mangoes at the rate of $9 per kg and there by losses 20%. At what price per kg, he should have sold them to make a profit of 5% ?
Solution :
Let x be the cost price.
Selling price = $9 per kg
x - 20% of x = 9
80% of x = 9
x = 9/0.80
x = 11.25
To make 5% profit, the selling price will be
= 105% of 11.25
= 1.05(11.25)
= 11.81
Example 2 :
A property dealer sells a house for $630000 and in the bargain makes a profit of 5%. Had he sold it for $500000 then what percentage of loss or gain he would have made ?
Solution :
Selling price of a house = 630000
Let x be the cost price.
105% of x = 630000
x = 630000/1.05
x = 600000
So, the cost price is 600000.
New selling price = 500000
Cost price > selling price
Loss = Cost price - Selling price
Loss = 100000
Loss % = (Loss / Cost price)⋅100
= (100000/600000)⋅100
= 16.67%
Example 3 :
A shopkeeper sells one transistor for $840 at a gain of 20% and another for $960 at a loss of 4%. His total gain or loss percent is :
Solution :
Let x be the cost price.
Selling price of one transistor = $840
120% of x = 840
x = 840/1.20
x = 700
Selling price of another transistor = $960
96% of x = 960
x = 960/0.96
x = 1000
Total cost of two transistors = 700 + 1000
= 1700
Total selling price = 840 + 960
= 1800
Selling price > Cost price
profit = 1800 - 1700
Profit = 100
profit % = (profit / Cost price)⋅100
= (100/1700)⋅100
= 5.88%
After having gone through the stuff given above, we hope that the students would have practiced problems in profit and loss.
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