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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.

i am amaan shaikh i am study in class 8 in ambika public school

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Jim B. | Experienced teacher and author tutoring in Math and Computer TopicsExperienced teacher and author tutoring ...
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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.
Phillip R. | Top Notch Math and Science Tutoring from Brown Univ GradTop Notch Math and Science Tutoring from...
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%