Question

A shopkeeper made a loss of Rs.20 when he sold a bag at 20% discount if he had sold it at 10% discount he would have gained 8% find the market price of the bag

Answer 1

Given:

A shopkeeper made a loss of Rs.20 when he sold a bag at 20% discount if he had sold it at 10% discount he would have gained 8%  

To find:

Find the market price of the bag

Solution:

From given, we have,

A shopkeeper made a loss of Rs.20 when he sold a bag at 20% discount if he had sold it at 10% discount he would have gained 8%.

Let us denote the marked price, selling price & cost price as M, S & C respectively.

When shopkeeper sells at 20% discount then he suffers a loss of Rs.20 then we have

S = (1 − 20/100) M = 0.8M  

C − S = 20

⇒ C = 20 + 0.8 M ....(1)

When shopkeeper sells at 10% discount then he makes a profit of 8% then we have

S = ( 1 − 10/100) M = 0.9 M  

S = ( 1 + 8/100) C  

⇒ C = 0.9M/1.08 ........(2)  

As the cost price of the bag doesn't change hence equating (1) & (2), we get

20 + 0.8M = 0.9M/1.08

21.6 + 0.864M = 0.9M

0.036M = 21.6

M = 600

Therefore, the market price of the bag is Rs. 600