# Question regarding profit & loss:

Q: Mr. A wants to sell his watch at 20% profit. He bought it at 10% less and sold it at Rs 30 less, but still managed to gain 20%. What is the cost price of the watch.

My approach:

1: Since at the time of buying the watch he got 10% discount it must be the Marked Price over which he got this discount.

2: He must have got Rs 30 less on Marked Price as getting Rs 30 off on Cost Price would not lead him to earn 20% profit & getting 30 off on selling price makes no sense.

But this approach is failing (as the answer is not getting matched) please help

• Please provide a suitable reason before down voting - just to prove your own mental might & stupidity of the question (if it is really there).

Let $x$ be marked price. Cost Price = Price at which Mr. A purchased = $0.9x$ (He got it at 10% discount)

He sold it at Rs. 30 less, so Selling Price = $x-30$

Profit = $(x-30)-(0.9x)$= $0.1x -30$ Profit % = $100 ( 0.1x-30)/(0.9x)$

$20/100 = ( 0.1x-30)/(0.9x)$ $0.18x = 0.1x - 30$

$0.08x = -30$

Not possible, so question seems wrongly stated.

EDIT: Sorry for the mistake. Previously I wrote +30 instead of -30.

• How did -30 became +30 in the 4th last step? Commented Oct 26, 2017 at 14:44
• @Gaurav I am sorry for the mistake. Yes, indeed the question seems to be invalid. Commented Oct 26, 2017 at 14:53
• Even I thought it to be invalid but this was asked in a competitive exam (SSC CGL), here is the solution, check it & see if you can make some sense out of it meritanswers.com/questions/… Commented Oct 26, 2017 at 15:06
• @Gaurav They have arbitrarily assigned the selling price to be 120% of marked price. It is a VERY badly stated question. Commented Oct 26, 2017 at 15:11
• Got this entire thing but in a slightly twisted way: Initially A thought that the C.P would be X & he would sell it at 1.2X (making him earn 20% profit & that would be his S.P at that stage ). Surprisingly he found that he had been offered the commodity at 10% discount - now he throws 30 RS discount on his initial S.P 1.2X & finally he would earn 20% profit on his C.P i.e. 0.9x Commented Oct 26, 2017 at 17:26