Undiscounted Shirt Price Calculation with Discount and Loss
Let the undiscounted price (original marked price) of the shirt be denoted by P.
Cost Price Calculation from Discount
The shirt was initially bought by the seller at a 10% discount. This means the seller's cost price (CP) was 90% of the undiscounted price (P): $CP = P \times (1 - 0.10) = 0.90P$
Selling Price to Cost Price Relation
The shirt was then sold to a friend at a 10% loss. The selling price (SP) is given as Rs. 729.00. The loss is calculated based on the cost price (CP). $SP = CP \times (1 - 0.10) = 0.90 \times CP$
Substitute the known SP:
$729 = 0.90 \times CP$
Solve for CP:
$CP = \frac{729}{0.90} = \frac{7290}{9} = 810$
The seller's cost price was Rs. 810.
Undiscounted Price Calculation
Now, we use the cost price (CP) found and the relationship from the initial purchase ($CP = 0.90P$):
$810 = 0.90P$
Solve for the undiscounted price (P):
$P = \frac{810}{0.90} = \frac{8100}{9} = 900$
The undiscounted price of the shirt was Rs. 900.
Important Questions from Profit & Loss (Notes)
- A person incurs a loss of 10% by selling a watch for Rs. 450. At what price should the watch be sold to earn 10% profit?
- A shopkeeper bought an item for ₹7825 and marked it at 30% higher than the cost price. If he sells the item by allowing 20% discount, then his profit percentage will be :
- A bought an article at a certain price and sold it at 10% profit. B bought the same article at a price 10% lesser than A and sold it at ₹18 lesser than A. B's gain percentage in this deal is 20%. At what price B bought the article?
- A dealer buys two articles X and Y for ₹500 each. He marks each of them at the same price. He sells X by giving two successive discounts of 50% and 28% and still earns ₹958 as profit. If he sells Y at a single discount of 77%, then what is the profit percentage on Y?
- A shopkeeper earned a profit (in ₹) by selling an item, which is three times the discount offered (in ₹). If the discount offered is 6.25%, what is his profit percentage ?
