Question

A shopkeeper fixes the selling price of his goods at 60% above the cost price. He sells half of this stock at this price, a quarter of his stock at a discount of 25% on the original selling price, and the rest at a discount of 50% on the original selling price. Find the gain percent altogether.

Answer 1

Let the cost price of each article bought = Rs.100.
Let the number of article bought = x
M.P. of the article
= Rs.100 + 60% of Rs.100
= Rs. 100 + `(60/100 xx 100)`
= Rs.160
Number of articles sold at Rs.160 = `x/(2)`
∴ S.P. of `x/(2)`articles
= Rs.`(160 xx x/(2))`
= Rs.80x
Discount
= 25% on Rs.160
= `(25)/(100) xx 160`
= Rs.40
∴ S.P.
= Rs.160 - Rs.40
= Rs.120
Remaining number of articles scold at Rs.120
= `x - x/(2) - x/(4) = x/(4)`

∴  S.P. of `x/(4)`articles

= Rs.`(120 xx x/(4))`
= Rs.30x
Discount
= 50% on Rs.160
= `(50)/(100) xx 160`
= Rs.80
∴  S.P. = Rs.160 - Rs.80
= Rs.80
Number of articles sold at Rs. = `x/(4)`
∴  S.P. of `x/(4)`articles

= Rs.`(80 xx x/(4))`
= Rs.20x
Total S.P. of all articles 
= Rs.80x + Rs.30x + Rs.20x
= 130x
Profit
= S.P. - C.P.
= Rs.130x - Rs.100x
= Rs.30x
So,profit %
= `"profit"/"C.P." xx 100`

= `(30x)/(100x) xx 100`
= 30%
Hence, the gain percent altogether is 30%.