Vinod sold a watch to Arun at a gain of 12% and Arun had to sell it to Manoj at a loss of 5%.

Solution:

Let the CP of the watch for Vinod be ₹x.

SP = Gain + CP

$=12 \%$ of $\mathrm{CP}+x$

$=\frac{12}{100} x+x$

$=₹ \frac{112}{100} x$

Now,

SP of the water for Vinod will be the CP of the watch for Arun.

SP of the watch for Arun

$=\mathrm{CP}-$ Loss

$=\frac{112}{100} x-5 \%$ of $\frac{112}{100} x$

$=\frac{112}{100} x-\frac{5}{100}\left(\frac{112}{100} x\right)$

$=\frac{112}{100} x\left(1-\frac{5}{100}\right)$

$=₹ \frac{112}{100} x\left(\frac{95}{100}\right)$

SP of the watch for Arun will be the CP of the watch for Manoj.

But, CP of the watch for Manoj = ₹3,990

So,$\frac{112}{100} x\left(\frac{95}{100}\right)=3990$

$\Rightarrow x=\frac{3990 \times 100 \times 100}{11 \times 95}=3750$

Thus, Vinod paid ₹3,750 for the watch.