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# Mohan sold a watch to Karim at a gain of $10\%$ and Karim sold it to Rahim at a gain of $4\%$. If Rahim pays him Rs $14300$ for it. Then for how much did Mohan purchase it?

Last updated date: 16th May 2024
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Hint: In this problem we have to find the cost price of the watch that Mohan purchased it. We will use the formula to find cost price when profit and selling price is given. When CP and loss or profit percent is given then we use this formula, $SP = CP \times \dfrac{{(100 \pm gain/loss\% )}}{{100}}$.
This problem is based on the concept of Profit and Loss on selling or buying an item.
Cost price (C.P.) is the actual price at which an item is purchased. When the item is sold at a higher price then there is profit and when it is sold at a lower price, there is loss. The price at which it is sold is called the selling price ( S. P.).

Complete step by step solution:
The given problem says that Mohan sold a watch to Karim at a gain of $10\%$ and Karim sold it to Rahim at a gain of $4\%$. If Rahim pays him Rs. $14300$ for it.
Let the cost price of the watch which Mohan purchased be $x$.
Profit on watch when Mohan sold to Karim $=$$10\%$
Selling price ( SP): when CP and profit percent is given by formula
$SP = CP \times \dfrac{{(100 + gain\% )}}{{100}}$
Hence,
$SP = x \times \dfrac{{(100 + 10)}}{{100}} = \dfrac{{110x}}{{100}}$
Thus, Karim buys at Rs. $\dfrac{{110x}}{{100}}$
Now Karim is sold to Rahim at $4$ percent profit.
Hence
$SP = \dfrac{{110x}}{{100}} \times \dfrac{{(100 + 4)}}{{100}} = \dfrac{{104 \times 11x}}{{1000}}$
But Rahim pays Rs. $14300$
Therefore, $\dfrac{{104 \times 11x}}{{1000}} = 14300$
Cross multiply the above numerator and denominator to get the value ‘x’, then
On solving, we get
$x = \dfrac{{14300 \times 1000}}{{104 \times 11}}$
Hence $x = 12500$
Since, the cost price of the watch which Mohan purchased be $x$
Therefore, Mohan pays Rs. $12500$ for the watch.
Hence, Mohan sold a watch to Karim at a gain of $10\%$ and Karim sold it to Rahim at a gain of $4\%$. If Rahim pays him Rs. $14300$ for it. Mohan purchased it for Rs. $12500$
So, the correct answer is “ Rs. $12500$”.

Note: Cost Price is the actual price at which goods or services are purchased.
Selling price is the actual price at which same goods or services are sold.
Profit $=$ $SP - CP$
Loss $=$ $CP - SP$
When SP and loss or profit percent is given then $CP = SP \times \dfrac{{(100 \pm gain/loss\% )}}{{100}}$.