A shopkeeper sells his goods at a profit of 10%. If he had purchased it at 20% less and sells it at Tk. 10 more, he had a gain of 40%. Find the cost price of the goods.

Question: A shopkeeper sells his goods at a profit of 10%. If he had purchased it at 20% less and sells it at Tk. 10 more, he had a gain of 40%. Find the cost price of the goods.

Solution:
Let the C.P of an article is 100.
ATQ,
S.P will be 110 ..............(1)
If he has purchased it at 20% less, the new C.P = 100 - 20= 80

If the C.P is 80, then he earns a profit of 40% and sells the article at Tk. 10 more than the previous price.
So, when he earns 40% on the new C.P then the profit = (40/100) × 80 = 32

That means if the C.P = 80, the S.P = 80 + 32 = 112 ............(2)

Compare equation 1 and 2, and we get,
The difference between S.P is = 2
But ATQ, it should be 10, i.e., multiple of 5
So, we need to multiply the actual value with 5 then we get actual cost price.
Hence, the C.P of the article is = 100 × 5 = 500