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 marked price of bag.
Answers
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
It will cost ₹10
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