I had bought a shirt at 10% discount which I sold to a friend at a loss of 10%. If the friend paid me ₹729-00 for the shirt, what was the undiscounted price of the shirt?
The shirt was bought at a 10% discount. So, the cost price (price I bought it for) is:
Cost Price (CP) = U – 10% of U = U – 0.10U = 0.90U.
I sold this shirt to a friend at a loss of 10% on the price I bought it for (the CP).
The friend paid ₹729-00. This is the selling price (SP).
The loss is calculated on the CP.
Loss = 10% of CP = 0.10 * CP.
Selling Price (SP) = CP – Loss = CP – 0.10 * CP = 0.90 * CP.
We are given that the friend paid ₹729, so SP = ₹729.
729 = 0.90 * CP
To find CP, divide 729 by 0.90:
CP = 729 / 0.9 = 7290 / 9 = 810.
So, the cost price (the price I bought the shirt for) was ₹810.
Now, we need to find the undiscounted price U, knowing that CP = 0.90U.
810 = 0.90 * U
To find U, divide 810 by 0.90:
U = 810 / 0.9 = 8100 / 9 = 900.
The undiscounted price of the shirt was ₹900.
Let’s verify:
Undiscounted price = ₹900.
10% discount = 10% of 900 = 0.10 * 900 = ₹90.
Price after discount (CP) = 900 – 90 = ₹810. (This is the price I bought it for).
Sold at a loss of 10% on CP:
Loss amount = 10% of 810 = 0.10 * 810 = ₹81.
Selling Price (SP) = CP – Loss amount = 810 – 81 = ₹729.
This matches the amount the friend paid.
– Loss is calculated on the cost price (the price at which the seller bought the item).
– Selling Price = Cost Price – Loss.
– If something is sold at X% discount, the selling price is (100-X)% of the original price.
– If something is sold at Y% loss, the selling price is (100-Y)% of the cost price.