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 per cent altogether.

Answer 1

Let the cost price of each article bought = Rs.100.
Let the number of articles bought = x
M.P. of the articles = Rs.100 + 50% of Rs.100
= Rs.100 + `(50/100 xx 100)`
= Rs.150
Number of articles sold at Rs,150 = `x/(2)`
∴ S.P. of `x/(2)` articles 
= Rs. `(150 xx x/(2))`
= Rs.75x
Discount = 20% on Rs.150
= `(20)/(100) xx 150`
= Rs.30
∴ S.P.
= Rs.150 - Rs.30
= Rs.120
Remaining number of articles sold at Rs.120
= `x - x/(2) - x/(4) - x/(4)`

∴ S.P. of `x/(4)  "aricles"`
= Rs.`(120 xx x/(4))`
= Rs.30x
Discount
= 36% on Rs.150
= `(36)/(100) xx 150`
= Rs.54
∴ S.P.
= Rs.150 - Rs.54
= Rs.96
Number of articles sold at Rs. = `x/(4)`
∴ S.P. of `x/(4)` articles
= Rs.`(96 xx x/(4))`
= Rs.24x
Total S.P. of all articles
= Rs.75x + Rs.30x + Rs.24x
= 1129x
Profit
= S.P. - C.P.
=Rs.129x - Rs.100x
= Rs.29x
So, profit % 
= `"Profit"/"C.P." xx 100`

= `(29x)/(100x) xx 100`
= 29%
Hence, the gainpercent altogether is 29%.