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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

### 2 Answers by Expert Tutors

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...
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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%