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Question
A trader fixes the selling price of his goods at 50% above the cost price. He sells half of his stock at this price, a quarter of his stock at a discount of 20% on the original selling price, and the rest at a discount of 36% on the original selling price. Find the gain percent altogether.
Solution
Let the C.P. of each article bought = Rs.100
Let the number of articles bought = x
∴ C.P. of the articles = Rs.100x
M.P. of the articles
= Rs.100 + 50% of Rs.100
= Rs.150
Stage 1 :
No. of articles sold at Rs.150 = `x/(2)`
∴ S.P. of `x/(2)`articles
= Rs.`(150 xx x/2)`
= Rs.75x
Stage 2 :
Discount
= 20% of Rs.150
= `(20)/(100) xx "Rs."150`
= Rs.30
∴ S.P.
= Rs.150 - Rs.30
= Rs.120
No. of articles sold at Rs.120 = `x/(4)`
∴ S.P. of `x/(2)`articles
= Rs.`(120 xx x/4)`
= Rs.30x
Stage 3 :
Discount
= 36% of Rs.150
= `(36)/(100) xx "Rs."150`
= Rs.54
No. of articles sold at Rs.96 = `x/(4)`
∴ S.P. of `x/(2)`articles
= Rs.`(96 xx x/4)`
= Rs.24x
Total S.P. of all articles
= Rs.75x + Rs.30x + Rs.24x
= Rs.129x
∵ S.P. > C.P., therefore there is a gain
Gain
= Rs.129x - Rs.100x
= Rs,29x
Gain %
= `"gain"/"C.P." xx 100`
= `(29x)/(100x) xx 100`
= 29%.
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