Question

# A dealer buys a wrist watch for Rs. 225 and spends Rs. 15 on its repairs. If he sells the same for Rs. 300, find his profit(in percent).

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Hint: We will use the fact that gain is equal to selling price subtracted from cost price, i.e. gain= S.P -C.P. Gain percentage is the amount of gain per 100 units of C.P. Using the unitary method, we will find the gain percentage . We will also use the formula, $gain\%=\dfrac{gain}{C.P}\times 100$ to get the gain%.

We have the cost at which the wrist watch was purchased by the dealer = Rs. 225
The overhead expenses that were taken up by the dealer = Rs. 15
The amount for which the wrist watch was sold by the dealer = Rs. 300
Hence the gain earned by the dealer = Rs 300-Rs (225+15) = Rs. (300-240) =Rs. 60
(Because the overhead charges are also taken up by the dealer, so, they also go into the cost price)
Hence the gain earned by the dealer is equal to Rs.60
Gain percentage is defined as the amount of gain earned per 100 units of cost price.
We have, the gain on Rs 60 of C.P = Rs. 240
Hence, we have,
The gain on Re. 1 of C.P $=\dfrac{60}{240}=\dfrac{1}{4}$
Hence gain per Rs. 100 of C.P $=\dfrac{1}{4}\times 100=25\%$

Hence the gain percentage of the dealer = 25%

Note: We can directly calculate gain using the formula,
$gain\%=\dfrac{gain}{C.P}\times 100$
Substituting the values of gain and C.P, we get,
$gain\%=\dfrac{60}{240}\times 100=25\%$
Some students make mistakes by writing the total cost price as Rs. 225 - Rs. 15, but this is wrong as the cost spent for repair must be added to the cost price and not subtracted.