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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

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