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raju purchased a watch at 20% discount on its marked price but sold it at marked price.find the gain percent of raju on this transaction.

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2 Answers

Let P be the marked price,
then the cost to Raju was   (0.8)P, which represents a 20% discount.
 
When Raju sold the watch, his profit was P - .8P = 0.2 P
 
The percent gain for Raju = (Profit/Cost)* 100 = (.2p/.8P)*100 = 25%
 
Plug in some numbers to make sure this makes sense:
 
If the marked price is $100, Raju spends $80. He sells it for $100, so he makes $20 on his $80 investment, and $20 is 25% of $80, so this answer makes sense.
The price is not given. We only know the watch was bought for an amount that is 20% less than the original price.
Because this is a per cent question and per cent is based on 100, it is simple to pick $100 as the original or marked price. We can make up a number because the answer will be the same no matter what the price is.
So 20% of $100 is $20. Therefore he paid $100 - $20 = $80
He then sold it at the original price $100.
This means he got $20 more than he paid.
So the question asks, how does the amount gained ($20) compare to the price he paid ($80) and we need to express the answer as a per cent.
So we divide $20 / $80 = 1/4 = .25 = 25%
In summary, he got a 20% discount but earned a 25% gain.
 
We could do this problem in general terms as well rather than using a made up price of $100 as follows.
Let P = the original price
Then he paid 80% of P = .8P
His gain is (P - .8P) / (.8P) = .2P/.8P = .2/.8 = 1/4 = 25%

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