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A fruit seller had some apples. He sells 40% of them and still has 420 apples. How many apples did he have originally?
600
700
800
900
700
Since 40% are sold, 60% remain. Think of 60% as 6 parts out of 10. If 6 parts = 420, then 1 part = 70. Total (10 parts) = 700.
Percentage of apples sold = 40%, Remaining apples = 420
Total=100%тИТPercentageSoldRemainingтАЛ
Since 40% are sold, 60% remain. Think of 60% as 6 parts out of 10. If 6 parts = 420, then 1 part = 70. Total (10 parts) = 700.
Students often calculate 40% of 420 instead of recognizing that 420 represents the remaining 60% of the original quantity.
Define the unknown
Let the original number of apples be x. Since 40% were sold, the percentage of apples remaining is 100%тИТ40%=60%.
60%┬аof┬аx=420
Set up the equation
Express 60% as a fraction 0.6 or 10060тАЛ and equate it to the given count of 420.
10060тАЛ├Чx=420
Solve for x
Multiply both sides by 100 and divide by 60 to isolate x: x=60420├Ч100тАЛ.
x=7├Ч100=700
B is correct because calculating 60% of 700 results in 420, which matches the remaining apples given in the problem.
This concept of 'Remaining value equals (100 - x)% of total' is foundational for Profit and Loss problems where you find the Cost Price after a discount or sale.
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