Vinod sold a watch to Arun at a gain of 12% and Arun had to sell it to Manoj at a loss of 5%. If manoj paid ₹ 3990 for it, how much did vinod pay for the watch?

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Solution

Let the CP of the watch for Vinod be ₹x.
SP = Gain + CP
$= 12 % of CP + x = \frac{12}{100} x + x = ₹ \frac{112}{100} x$
Now,
SP of the water for Vinod will be the CP of the watch for Arun.
SP of the watch for Arun
= CP − Loss
$= \frac{112}{100} x - 5 % of \frac{112}{100} x = \frac{112}{100} x - \frac{5}{100} (\frac{112}{100} x) = \frac{112}{100} x (1 - \frac{5}{100}) = ₹ \frac{112}{100} x (\frac{95}{100})$
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,
$\frac{112}{100} x (\frac{95}{100}) = 3990$
$\Rightarrow x = \frac{3990 \times 100 \times 100}{112 \times 95} = 3750$
Thus, Vinod paid ₹3,750 for the watch.

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