Question

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 Rs3990 for it, how much did Vinod pay for the watch?

Answer 1

Hint: According to the given, Cost Price of watch by Manoj = Selling Price of watch by Arun. Calculate the CP of watch by Arun. CP of watch by Arun = SP of watch by Vinod. Calculate the CP of watch by Vinod.

Complete step-by-step answer:
CP = Cost Price and SP = Selling Price

CP of watch by Manoj = SP of watch by Arun= Rs3990

Given: Loss for Arun is 5%
Loss%=5%

We know CP – CP × loss% = SP,

CP of watch by Arun = $\dfrac{{{\text{SP}}}}{{\left( {1 - {\text{loss % }}} \right)}}$
CP of watch by Arun = $\dfrac{{3990}}{{1 - \dfrac{5}{{100}}}} = \dfrac{{100}}{{95}} \times 3990$
CP of watch by Arun = Rs4200

Now, CP of watch by Arun = SP of watch by Vinod

SP of watch by Vinod = Rs4200

Given: Gain for Vinod is 12%
Gain%=12%

We apply, CP + CP × gain% = SP

Hence,
 CP of watch by Vinod = $\dfrac{{{\text{SP}}}}{{\left( {1 + {\text{gain % }}} \right)}}$
 CP of watch by Vinod = $\dfrac{{4200}}{{1 + \dfrac{{12}}{{100}}}} = \dfrac{{100}}{{112}} \times 4200$
 CP of watch by Vinod = Rs.3750

Therefore Vinod paid Rs.3750 for the watch.

Note: The key in such problems is to identify that CP of watch by Manoj = SP of watch by Arun and CP of watch by Arun = SP of watch by Vinod. To find the Cost Price we use its formula. Gain percent is added to cost price to determine selling price and vice versa for loss percent.