Question

A refrigerator was sold at a gain of 12%. Had it been sold for Rs. 357 more, the gain would have been 15%. Find the cost price of the refrigerator.

Answer 1

Hint- In this question, we need to determine the cost price of the refrigerator such that if it had been sold at Rs. 357 than the initial selling price then, the gain percentage would be 15% instead of old 12% gain for which we need to use two parameters, i.e., one for the cost price and the other for the selling price and satisfy the conditions given in the question.


Complete step by step solution:

Let the initial selling price be $x$ and cost price be $y$.
According to the question, there are two situations, and both are having different gain percentages.

As a refrigerator was initially sold at a gain of 12% so, using the formula ${\text{Profit % = }}\left( {\dfrac{{{\text{Profit}}}}{{{\text{Cost Price}}}}} \right) \times 100$ we get,

$
  12 = \left( {\dfrac{{x - y}}{y}} \right) \times 100 \\
  \left( {x - y} \right) \times 100 = 12y \\
  x - y = \dfrac{{12y}}{{100}} \\
  x - y = 0.12y \\
  x = 0.12y + y \\
  x = 1.12 - - - - \left( i \right) \\
 $

Now, the selling price has increased by Rs. 357 then the new selling price is $x + 357$ and the new gain percentage is 15%. So, again using the same formula ${\text{Profit \% = }}\left( {\dfrac{{{\text{Profit}}}}{{{\text{Cost Price}}}}} \right) \times 100$ we get,
\[
  15 = \left( {\dfrac{{x + 357 - y}}{y}} \right) \times 100 \\
  15y = \left( {x + 357 - y} \right) \times 100 \\
  x + 357 - y = \dfrac{{15y}}{{100}} \\
  x + 357 - y = 0.15y \\
  x + 357 = 1.15y - - - - \left( {ii} \right) \\
 \]

Now, substitute the value of $x$ from equation (i) into equation (ii) we get,

$
  x + 357 = 1.15y \\
  1.12y + 357 = 1.15y \\
  1.15y - 1.12y = 357 \\
  0.03y = 357 \\
  y = \dfrac{{357}}{{0.03}} \\
  y = \dfrac{{35700}}{3} \\
  y = 12500 \\
 $

Hence, the cost price of the refrigerator is Rs.12500.


Note: Students usually get confused between the cost price and marked price. Marked price is the normal price of the product 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.