Question

The marked price of an article is Rs 200. A discount of \[12\dfrac{1}{2}\% \] is allowed on the marked price and a profit of 25 % is made. What is the cost price of the article?
a) Rs.120
b) Rs.140
c) Rs.160
d) Rs.180

Answer 1

Hint: Discount Percentage = [Discount/Marked price] x 100
Selling Price = Marked price – Discount
\[SP = MP - \dfrac{{Discount\% }}{{100}} \times Discount\]
Profit, P = SP – MP
\[Profit\% = \dfrac{{Profit}}{{MP}} \times 100\]
\[CP = \dfrac{{100}}{{100 + profit\% }} \times SP\]

Complete step-by-step answer:
Marked price, MP = Rs.200
Discount% = 12.5%
\[SP = MP - \dfrac{{Discount\% }}{{100}} \times Discount\]
\[\begin{array}{l} = 200 - \dfrac{{12.5}}{{100}} \times 200\\ = 200 - 25\\ = 175\end{array}\]
Therefore,
Profit = 25%
\[\therefore CP = \dfrac{{100}}{{100 + profit\% }} \times SP = \dfrac{{175 \times 100}}{{125}} = Rs.140\]

Note: Some useful formula to remember.
Discount = Marked Price – Selling Price
And Discount Percentage = (Discount/Marked price) x 100
Profit or Gain = Selling price – Cost Price
Loss = Cost Price – Selling Price
Profit percentage = (Profit /Cost Price) x 100
Loss percentage = (Loss / Cost price) x 100
Profit, P = SP – CP; SP>CP
Loss, L = CP – SP; CP>SP