Question

A photography dealer ordered $60$ Model $X$ cameras to be sold for 250$each,whichrepresentsa$20$percentmarkupoverthedeale{r}^{\prime }sinitialcostforeachcamera.Ofthecamerasordered,$6$wereneversoldandwerereturnedtothemanufacturerforarefundof$50$ percent of the dealer's initial cost. What was the dealer's approximate profit or loss as a percent of the dealer's initial cost for the $60$ cameras?

• A. $7\%$ loss
• B. $13\%$ loss
• C. $7\%$ profit
• D. $13\%$ profit
• E. $15\%$ profit

Answer 1

The correct option is D $13\%$ profit

Given: $S.P.=250S.P.=\frac{120}{100}\times C.P.$

$S.P.=\frac{6}{5}C.P.C.P.=\frac{5}{6}S.P.$

Also, $6$ cameras were not sold and were returned for $50$% of $C.P.$

Loss$=6\times \frac{50}{100}\times \frac{5}{6}\times 250=625$ (negative)

So, he sold $54$ cameras

Profit$=54\times \frac{20}{100}\times C.P.$

$=54\times \frac{1}{5}\times \frac{5}{6}\times 250=2250$ ...(positive)

Total$=225-625$$=1625$ ...(Profit)

Percentage profit$=\frac{Profit}{TotalC.P.}\times 100$

$=\frac{1625}{60\times \frac{5}{6}\times 250}\times 100=\frac{1625}{125}=13$

Hence, the total profit is of $13\%$.