Problem Solving

A photography dealer ordered 60 Model X cameras to be sold for $250 each, which represents a 20% markup over the dealer's initial cost for each camera. Of the cameras ordered, 6 were never sold and were returned to the manufacturer for a refund of 50% 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

A photography dealer ordered 60 Model X cameras to be sold for $250 each, which represents a 20 percent markup over the dealer's initial cost for each camera. Of the cameras ordered, 6 were never sold and were returned to the manufacturer for a refund of 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

54 cameras yield a 20% profit, while 6 cameras suffer a 50% loss.
Average for all 60 cameras = (54*20 - 6*50)/60 = 780/60 = 13.

The correct answer is D.

Hi Experts ,

Can you please check and advise what will be the next.

S.P.( Selling Price)= $250

Profit %= 20%

Profit in $ = 20/100*250 = $50

so that means C.P.( Cost rice) = $200

Total S.P. of 54 camera = 54*250 = 13500

Now I don't understand this line 50 percent of the dealer's initial cost

Please advise .

Many thanks in advance.

SJ

Hi Mitch

Your method seems to be very quick.
But I am not able to understand the logic on this. Could you please elaborate.

eitijan wrote:Hi Mitch

Your method seems to be very quick.
But I am not able to understand the logic on this. Could you please elaborate.

This is a MIXTURE problem.

The 54 sold cameras each yield a profit of 20%.
Total profit for the 54 sold cameras = (54)(20).

Since the dealer receives only a 50% refund for the 6 unsold cameras, the 6 unsold cameras each suffer a loss of -50%.
Total loss for the 6 unsold cameras = (6)(-50).

The total profit for the 54 sold cameras is combined with the total loss for the 6 unsold cameras to form a MIXTURE of 60 cameras.
Total profit or loss for the mixture of 60 cameras = 54*20 - 6*50.

To determine the dealer's profit or loss, we calculate the AVERAGE profit or loss for the MIXTURE of 60 cameras.
Average profit or loss for the mixture of 60 cameras = (total profit or loss for the mixture)/(number of cameras) = (54*20 - 6*50)/60 = 13.

jain2016 wrote:
Now I don't understand this line 50 percent of the dealer's initial cost

Suppose the dealer paid $250 for each of these six cameras. Unable to sell them, the dealer asks the supplier for a refund. The supplier agrees to refund 50% of the cost, or $125 each, for the six cameras.

So the dealer LOSES $125 for each camera (... which is presumably better than just leaving the cameras in storage somewhere and losing the full $250 on each of them.)