An item is sold at a profit of 10%. Had it been bought for 10% less and sold for $10 less, the profit would have been 20%. What is the cost price of the item?
The Usual Method
Let the cost price of the article be $‘x’.
Hence selling price = 1.1x
New cost price = 0.9x
New selling price = 1.1x – 10
Hence profit at new selling price on new cost price =
(As given in the question)
Estimated Time to arrive at the answer = 45 seconds.
Note that the new cost price will be 90% of the original cost price. Hence the denominator in the formula to find profit % (Profit % = ) will be a multiple of 9 (in this case 0.9x)
Also note that since the new percentage profit being 20% – a whole number, the numerator (SP – CP) should also be a multiple of 9. Checking the options as follows:
Option New SP New CP Difference Remarks
a. 110 – 10 = 100 90 10 Not a multiple of 9
b. 1100 – 10 = 1090 900 190 Not a multiple of 9
c. 550 – 10 = 540 450 90 Multiple of 9
No need to check further as there cannot be more than one correct answer!
Estimated Time to arrive at the answer = 30 seconds.