Question

A refrigerator and a camera were sold for Rs. 12,000 each. The refrigerator was sold at a loss of 20% and the camera was sold at a gain of 20%. The entire transaction results in which of the following?
A. No loss, no gain
B. Loss of Rs. 1000
C. Gain of Rs. 1000
D. Loss of Rs. 2000

Answer 1

Hint: Find the cost price of the refrigerator and the camera and add them to get the total cost price. Similarly, find the total selling price. Use the formulae, $CP=\left( \dfrac{100}{100-L%} \right)\times SP$ and$CP=\left( \dfrac{100}{100-P%} \right)\times SP$ to find the required cost prices.

Complete step by step solution:
Let us first find the Cost price (CP) = x, of the refrigerator using the values,
Selling price (SP) = Rs. 12,000/-, Loss percentage (L%) = 20%.
Use the formula, $CP=\left( \dfrac{100}{100-L%} \right)\times SP$
$\begin{align}
  & CP=\left( \dfrac{100}{100-20} \right)\times 12,000 \\
 & x=\left( \dfrac{100}{80} \right)\times 12,000 \\
 & x=15,000
\end{align}$
Now, let us find the Cost price (CP) = y, of the camera using the values,
Selling price (SP) = Rs. 12,000/-, Profit percentage (P%) = 20%
Use the formula, $CP=\left( \dfrac{100}{100-P%} \right)\times SP$
$\begin{align}
  & CP=\left( \dfrac{100}{100+20} \right)\times 12,000 \\
 & y=\left( \dfrac{100}{120} \right)\times 12,000 \\
 & y=10,000
\end{align}$
Let us add the cost price of the refrigerator and the camera and find out the total cost price.
Total Cost price = x + y
                             = 15,000+10,000
                             = 25,000
Now, let us add the selling price of the refrigerator and camera and find the total selling price.
Total Selling price = 12,000+12,000
                                 = 24,000
Here, total cost price is Rs. 25,000/- and total selling price is Rs. 24,000/-. Subtracting the two will give us the value. Also, CP > SP, hence we will get a loss.
Loss = 25,000 – 24,000
         = 1,000
Hence, the transaction results in the loss of Rs. 1,000.

Note: Check which of the prices is greater, if the cost price is greater than selling price, we will incur a loss and if cost price is smaller than selling price, we will incur a profit. Also, the question gives the value of selling price including the loss and gain percent of the refrigerator and camera respectively. Always remember to put the units for the calculated value to avoid cancellation of marks.