Question

A man fixes the selling price of his goods at 50% above the cost price. He sells one-third of his stock at this price, one-third of his stock at a discount of 20% on the original selling price, and the rest at a discount of 40% on the original selling price. Find the gain percent altogether.

Answer 1

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/(3)`

∴ S.P. of `x/(3)`articles

= Rs.`(150 xx x/3)`
= Rs.50x
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/(3)`

∴ S.P. of `x/(3)`articles

= Rs.`(120 xx x/3)`
= Rs.40x
Stage 3 :
Discount
= 40% of Rs.150
= `(40)/(100) xx "Rs."150`
= Rs.60
∴ S.P.
= Rs.150 - Rs.60
= Rs.90
No. of articles sold at Rs.90 = `x/(3)`

∴ S.P. of `x/(3)`articles

= Rs.`(90 xx x/3)`
= Rs.30x
Total S.P. of all articles
= Rs.50x + Rs.40x + Rs.30x
= Rs.120x
∵ S.P. > C.P., therefore there is a gain
Gain
= Rs.120x - Rs.100x
= Rs.20x
Gain %
= `"gain"/"C.P." xx 100`

= `(20x)/(100x) xx 100`
= 20%.