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Question
By selling 80 bananas for Rs. 240 a fruit seller loses 25%. How many bananas should he sell for Rs.100 to gain 25%.
Solution
S.P. of 80 bananas = Rs.240
S.P. = `((100 - "Loss")/100) xx "C.P."`
⇒ 240 = `((100 - 25)/100) xx "C.P."`
⇒ 240 = `(75)/(100) xx "C.P."`
⇒ C.P. = `(240 xx 100)/(75)`
⇒ C.P. = Rs.320
So, C.P. of 80 bananas is Rs.320
∴ C.P. of 1 bananas
= Rs.`(320)/(80)`
= Rs.4
Let the number of bananas for sold for Rs.100 be x.
So, C.P. of x bananas = Rs.4x
Now, S.P. = `((100 + "Profit%")/100) xx "C.P".`
⇒ 100 = `((100 + 25)/100) xx 4x`
⇒ 100 = `(125)/(100) xx 4x`
⇒ 100 = `(5)/(4) xx 4x`
⇒ 100 = 5x
⇒ x = 20
Hence, he should sell 20 bananas for Rs.100 to gain 25%.
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