Question

In one shop, an article is marked 75% above the cost price but the purchaser is allowed a discount of 20% on the marked price. In another shop, a similar article is sold for Rs. 58 at a gain of 45%. What did the purchase pay for this article in the first shop?
A. $Rs.69$
B. $Rs.56$
C. $Rs.62$
D. $Rs.65$

Answer 1

Hint: In this question we have to find the selling price of an article in the first shop. Use formula for selling price as S.P.=$\left( {1 + \dfrac{{profit}}{{100}}} \right) \times C.P.$ also selling price S.P. = $\left( {1 - \dfrac{{{\text{discount}}}}{{100}}} \right) \times {\text{Marked Price}}$

Complete step-by-step answer:

Let marked price be M.P., Cost price be C.P. and selling price be S.P.
Now in Shop 2
Selling price = Rs 58; profit = 45%
$
  S.P. = \left( {1 + \dfrac{{45}}{{100}}} \right) \times C.P. \\
  58 = \left( {1 + 0.45} \right) \times C.P. \\
  58 = 1.45 \times C.P. \\
  C.P. = 40 \\
$
In shop 1
$
  M.P = C.P\left( {1 + \dfrac{{75}}{{100}}} \right) \\
  M.P = 1.75 \times C.P \\
  M.P = 1.75 \times 40 = 70 \\
$
Now, selling price in shop 1 will be
 $
   = M.P. \times \left( {1 - \dfrac{{{\text{discount}}}}{{100}}} \right) \\
   = 70 \times \left( {1 - \dfrac{{20}}{{100}}} \right) \\
   = 70 \times 0.80 = 56 \\
$
Therefore, the selling price is 56.

Hence option (B) is the correct answer.

Note: In order to solve such problems related to selling price and cost price first of all check into the problem if both selling price and cost price are mentioned or not. If not start the solution by considering them in terms of some unknown value. Students must remember formulas for selling price.