A furniture dealer sold two chairs for $300 each. He made a profit of

To find Cost price of each chair 1: 1.25(CP) = 300 => CP(C1) = $240

To find Cost price of each chair 1: .75(CP) = 300 => CP(C2) = $400

Total CP = 240+400 = $640

Total SP = 300+300 = $600

Loss of $40, which is around 6%

IMO Option B

Cost Price of chair 1 = 300*100/125 = 240
Cost price of chair 2 = 300*100/75 = 400

Total cost price = 240+400 = 640
Total Selling Price = 600
Change percentage = (SP-CP/CP)*100
(600-640/640)*100
(-40/640)*100
-6.25 or 6% approx
So the seller made 6% loss in total.
Answer is B

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There is a General derived formula to find Net Profit/Loss Percentage; when Selling Price of both Goods is same

Net profit percentage
=(100*(x1+x2)+2*x1*x2 )/ (200+x1+x2)

Here x1 and x2 are Profit or Loss Percentages
If loss then it must be replaced with a negative sign

Replacing x1=25; x2=(-)25

We get 25/4 = 6.25

Solution:

For the chair for which he made a profit, let c = cost of that chair. So we have:

1.25c = 300

c = 240

For the chair for which he had a loss, let h = cost of that chair. So we have:

0.75d = 300

d = 400

Therefore, the total cost of the two chairs was 240 + 400 = $640, and the total revenue of the two chairs was 300 x 2 = $600. So his overall loss percentage is

(640 - 600)/660 x 100 = 40/660 x 100 = 2/33 x 100 = 200/33 ≈ 6

Answer: B

That should be 640 in the denominator, right ? not 660.

Also, I see people using the formula:(P%*L%)/100

(25*25)/100
which works fine here and gives the correct answer for this question.

Can you please confirm if this is a standard formula which can be used in any question having a similar set up.

Thank you!

Response:

660 was a typo, it should indeed be 640. Thanks for pointing it out.

For the formula (P%*L%)/100, it will work as long as the sale prices are equal. For a situation where this formula is not applicable, suppose that the dealer sold a piece of furniture for $300 and made 25% profit, but sold another piece of furniture for $750 and made a 25% loss. Then, the cost of the $300 piece is 300/1.25 = $240, and the cost of the $750 item is 750/0.75 = $1,000. Since the dealer spent 240 + 1000 = $1,240 and made only 300 + 750 = $1,050, his loss is 1,240 - 1,050 = $190. So, his loss is 190/1,240 ≈ 0.153, which corresponds to roughly 15.3%. As you can see, although he is making a 25% profit and a 25% loss, his overall loss is not 6.25%.

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