Question

A housewife paid Rs. 1260 for a handbag after a 37% discount. The original price of the handbag was
A) Rs 1500
B) Rs 1850
C) Rs 2000
D) Rs 1760

Answer 1

Cost Price (C.P.): Price at which an article is purchased.
Selling Price (S.P.): Price at which an article is sold by a shopkeeper.
Profit/Gain: The seller is said to be in profit, if selling price is greater than cost price.
Profit = S.P. - C.P.
{\text{Profit% = }}\left( {\dfrac{{{\text{Profit}}}}{{{\text{C}}{\text{.P}}{\text{.}}}}} \right) \times 100
Loss: The seller is said to be in loss, if the selling price is lesser than cost price.
Loss = C.P. – S.P.
{\text{Loss% = }}\left( {\dfrac{{{\text{Loss}}}}{{{\text{C}}{\text{.P}}{\text{.}}}}} \right) \times 100
Discount refers to the deduction in the cost price of a product.
Discount = Marked Price – Selling Price
Discount% = $\left( {\dfrac{{{\text{Discount}}}}{{{\text{ Marked Price}}}}} \right) \times 100$
We have to find the marked price.

Complete step by step answer:
Let the original price of handbag was = x
Selling price of handbag (S.P.) = Rs.1260
Discount = 37%
We know that,
Selling price = Marked Price – Discount
Discount = \dfrac{{\left( {{\text{Discount% }}} \right){\times}\left( {{\text{Marked Price}}} \right)}}{{100}}
$\begin{gathered} 1260 = x - 37\% {\text{ of }}x \\\ 1260 = x - \left[ {x \times \dfrac{{37}}{{100}}} \right] \\\ 1260 = x - \dfrac{{37x}}{{100}} \\\ 1260 = \dfrac{{100x - 37x}}{{100}} \\\ 1260 = \dfrac{{63x}}{{100}} \\\ x = \dfrac{{1260 \times 100}}{{63}} \\\ x = 20 \times 100 \\\ x = Rs2000 \\\ \end{gathered}$

So, the original price of the handbag was Rs 2000.
∴Option (C) is correct.

Note: Students usually get confused between the Cost price and Marked price. Marked price is the normal price of the thing without any discount or we can say the price printed on the item while the Cost price is the amount at which the shopkeeper buys the item.
∴Cost Price = Selling Price – Gain
or Cost Price = Selling Price + Loss
and Marked price = Selling price + Discount
If a trader sells goods at cost price but uses a weight of x kg instead of y kg (false weights) and makes profit. This profit can be calculated using the formula shown below:
Error = True weight – False weight
{\text{Gain% = }}\left[ {\dfrac{{{\text{Error}}}}{{\left( {{\text{True weight - Error}}} \right)}}{{ \times 100}}} \right]{\text{% }}