Question

Gurpeet sells two watches for Rs.1995 each, gaining \[15\% \] on one and losing \[15\% \] on the other. Find his gain or loss percent in his whole transaction?

Answer 1

Hint: We know that gain or loss is decided by the value of cost price and selling price. If C.P. is greater than S.P. Then he suffered loss and in reverse case he gained. So, this is the hint to find the total C.P. and S.P. we have S.P. already given in the problem. We will find the C.P. and then we will proceed.

Complete step-by-step answer:
We will tabulate the calculation of two different transactions to get the value of C.P. in both the cases.
Case 1: gain of 15%
given that, S.P.= 1995
%profit=15%
We know that,
 \[\% profit = \dfrac{{profit}}{{C.P.}} \times 100\]
But we know that, Profit=S.P.-C.P
So, \[\% profit = \dfrac{{S.P. - C.P.}}{{C.P.}} \times 100\]
Substituting the values,
 \[15 = \dfrac{{1995 - C.P.}}{{C.P.}} \times 100\]
Cross multiplying we get,
 \[\dfrac{{15}}{{100}}C.P. = 1995 - C.P.\]
Taking the C.P. on one side,
 \[0.15C.P. + C.P. = 1995\]
 \[1.15C.P. = 1995\]
 \[C.P. = \dfrac{{1995}}{{1.15}}\]
Multiplying both numerator and denominator by 100,
 \[C.P. = \dfrac{{1995 \times 100}}{{1.15 \times 100}}\]
 \[C.P. = \dfrac{{199500}}{{115}}\]
On dividing we get,
 \[C.P. = 1734.78\]

Case 2: loss of 15%
given that, S.P.= 1995
%loss=15%
We know that,
 \[\% loss = \dfrac{{loss}}{{C.P.}} \times 100\]
But we know that,
 \[loss = C.P. - S.P.\]
So, \[\% loss = \dfrac{{C.P. - S.P.}}{{C.P.}} \times 100\]
Substituting the values,
 \[15 = \dfrac{{C.P. - 1995}}{{C.P.}} \times 100\]
Cross multiplying we get,
 \[\dfrac{{15}}{{100}}C.P. = C.P - 1995\]
Taking the C.P. on one side,
 \[1995 = C.P - 0.15C.P.\]
 \[1995 = 0.85C.P.\]
 \[\dfrac{{1995}}{{0.85}} = C.P.\]
Multiplying both numerator and denominator by 100,
 \[C.P. = \dfrac{{1995 \times 100}}{{0.85 \times 100}}\]
 \[C.P. = \dfrac{{199500}}{{85}}\]
On dividing we get,
 \[C.P. = 2347.05\]
Now we have total S.P. equals to \[1995 + 1995 = 3990\]
total C.P. of the watches is \[1734.78 + 2347.05 = 4081.83\]
Now clearly we can say that Gurpreet suffers a loss.
Thus \[\% loss = \dfrac{{4081.83 - 3990}}{{4081.83}} \times 100\]
On calculating further,
 \[\% loss = \dfrac{{91.83}}{{4081.83}} \times 100\]
On multiplying by 100 we get,
 \[\% loss = \dfrac{{9183}}{{4081.83}}\]
On dividing we get,
 \[\% loss = 2.249 \simeq 2.25\% \] .
This is the loss percent in the whole transaction.

Note: Here just note that the C.P. is different for both the watches but the S.P. is same. Don’t get confused. Whenever we face problems like these, we should cross check the available data. That is cost price, selling price and either profit or loss is incurred. We definitely use standard formulas for the solution. Sometimes the C.P. are the same but S.P. is different but we will go with the same formula and will reach the answer.