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A shopkeeper sells an item for Rs. 480 making a profit of 20%. What was the cost price?
Rs. 400
Rs. 380
Rs. 420
Rs. 450
Rs. 400
Use the fraction method: 20% profit means 120%=6/5 of CP. Since 6 units = 480 (one unit = 80), then 5 units = 5├Ч80=400.
Selling Price (SP) = 480, Profit percentage = 20%.
CP=100+Profit%SP├Ч100тАЛ
Use the fraction method: 20% profit means 120%=6/5 of CP. Since 6 units = 480 (one unit = 80), then 5 units = 5├Ч80=400.
A common mistake is calculating 20% of the selling price (480) and subtracting it, which results in 384 instead of the correct cost price.
Identify given variables
We are given the Selling Price SP=480 and the Profit percentage P=20%.
SP=480,P=20%
Set up the Cost Price formula
To find the original cost price before profit, use the relation CP=SP├Ч100+P100тАЛ.
CP=100+20480├Ч100тАЛ
Calculate the result
Simplify the denominator: 100+20=120. Now divide: 480/120=4. Multiply by 100 to get the final result.
CP=120480├Ч100тАЛ=4├Ч100=400
A is correct because the calculation of 480/1.2 yields exactly 400.
This concept of base-value calculation is essential for 'Discount' problems where you calculate the Marked Price from the Selling Price.
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