Answer

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**Hint:**When a product is purchased in the view of selling it to the consumer in order to do business then, the price in which the product is bought by the seller is known as the cost price of the product and the price in which the seller sells the product to the consumer is known as selling of the product for the seller. If the selling price of the product is greater than the cost price of the product, then the difference in the prices can be termed as the profit or the gain on the product while at the same time if the selling price is less than the cost price of the product, then the difference in the price is known as the loss on the product. Profit percent or loss percent of a product is always calculated on the cost price of the product. In this question, it is already mentioned the salesman has gained a profit on a watch and would have gained more profit if the selling price would have been raised.

**Complete step by step solution:**Given that the salesman has gained a profit, which means that the selling price is more than the cost price

Let us assume \[S.P = x\] and cost price C.P is fixed in both the case

Hence we can write for the 15% profit.

\[

P\% = \dfrac{{SP - CP}}{{CP}} \times 100 \\

15\% = \dfrac{{x - CP}}{{CP}} \times 100 \\

\dfrac{x}{{CP}} - 1 = \dfrac{{15}}{{100}} \\

\dfrac{x}{{CP}} = 0.15 + 1 \\

CP = \dfrac{x}{{1.15}} - - - - \left( i \right) \\

\]

Now when the selling price is raised by Rs.48, the profit percentage also increases

\[

P'\% = 18\% \\

SP' = x + 48 \\

\]

Hence we can write

\[

P'\% = \dfrac{{SP' - CP}}{{CP}} \times 100 \\

18 = \dfrac{{\left( {x + 48} \right) - CP}}{{CP}} \times 100 \\

\dfrac{{x + 48}}{{CP}} = \dfrac{{18}}{{100}} + 1 \\

\dfrac{{x + 48}}{{CP}} = 1.18 \\

CP = \dfrac{{x + 48}}{{1.18}} - - - - (ii) \\

\]

Since the selling price is being increased on the same cost price, hence we can say cost price is the same in both the cases; hence we can say\[\left( i \right) = \left( {ii} \right)\], by equating both the equations

\[

\left( i \right) = \left( {ii} \right) \\

\dfrac{x}{{1.15}} = \dfrac{{x + 48}}{{1.18}} \\

1.18x = 1.15x + 55.2 \\

0.03x = 55.2 \\

x = Rs.1840 \\

\]

Hence the selling price is Rs.1840

Now put the value of \[x\]which is the selling price in equation (i), we get

\[CP = \dfrac{x}{{1.15}} = \dfrac{{1840}}{{1.15}} = Rs.1600\]

Hence the cost price of the watch is Rs.1600

**Note:**It is to be noted here that many a time, the marked price has been given in the question instead of selling price. So, be careful while reading the question as the marked price is the price that has been marked on the product by the seller, but the selling price is the price of the product which the seller actually gets for the product after discount.

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