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 + ${\displaystyle (\frac{50}{100}\times 100)}$
= Rs.150
Number of articles sold at Rs,150 = ${\displaystyle \frac{x}{2}}$
∴ S.P. of ${\displaystyle \frac{x}{2}}$ articles 
= Rs. ${\displaystyle (150\times \frac{x}{2})}$
= Rs.75x
Discount = 20% on Rs.150
= ${\displaystyle \frac{20}{100}\times 150}$
= Rs.30
∴ S.P.
= Rs.150 - Rs.30
= Rs.120
Remaining number of articles sold at Rs.120
= ${\displaystyle x-\frac{x}{2}-\frac{x}{4}-\frac{x}{4}}$

∴ S.P. of ${\displaystyle \frac{x}{4} \text{aricles}}$
= Rs.${\displaystyle (120\times \frac{x}{4})}$
= Rs.30x
Discount
= 36% on Rs.150
= ${\displaystyle \frac{36}{100}\times 150}$
= Rs.54
∴ S.P.
= Rs.150 - Rs.54
= Rs.96
Number of articles sold at Rs. = ${\displaystyle \frac{x}{4}}$
∴ S.P. of ${\displaystyle \frac{x}{4}}$ articles
= Rs.${\displaystyle (96\times \frac{x}{4})}$
= 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 % 
= ${\displaystyle \frac{\text{Profit}}{\text{C.P.}}\times 100}$

= ${\displaystyle \frac{29x}{100x}\times 100}$
= 29%
Hence, the gainpercent altogether is 29%.