Question

A merchant buys goods at 25% off the list price. He desires to mark the goods such that he can give a discount of 20% on the marked price and still clear a profit of 25% on the selling price. The precent of the list price he must mark the goods is

Answer 1

Solution:-

Let the list price be Rs. 'x' 
Cost price = 25 % off on the list price
That will be 75 % of the list price 
= (75*x)/100
= 3x/4

The profit is 25 % on the selling price.
So, selling price = 125 % of the cost price.
= (125/100)*(3x/4)
= 15x/16

Let the marked price be Rs 'y'
If the merchant gives 20 % discount,
Then 80 % of marked price = Selling price
⇒ (80y/100) = 15x/16
After cross multiplying, we get.
1280y = 1500x
y = 1500x/1280
y = 75x/64

The percentage of the list price at which the merchant marks the goods =
(Marked Price - List Price)*100/List Price
⇒ (75x/64 - x/1)*100/x
Taking the L.C.M. of the denominators (64 and 1) and solving it, we get.
⇒ (11x*100)/64/x
⇒ (11x100/64)*(1/x)
⇒ 1100x/64x
⇒ 1100/64
= 17.1875 %

Answer