Question

A VCR and TV were bought for Rs 20,000 each. The shopkeeper made a loss of 10 percent on VCR and profit of 5 percent on TV. Find the overall gain or loss on the whole transaction?

Answer 1

Hint: Now we are given the cost price of each item. First we will assume the cost price to be x. Now we know that the loss = cost price – selling price and profit = selling price – cost price and percentage of profit or loss is given by $\dfrac{\text{profit/loss}}{\text{cost price}}\times 100$ . Hence we get the Cost price and hence the particular profit and loss. Hence using this we can calculate the total profit or loss.

Complete step by step answer:
Now we are given the cost price of VCR and TV which is Rs 20,000.
Now first let us consider VCR.
The cost price of VCR is Rs 20,000.
Now the shopkeeper made a loss of 10 percent on VCR.
Now let us say that the cost price of VCR was x Rs.
Hence we know that loss = x – 20,000.
Now we know that the loss percentage is given by $\dfrac{\text{loss}}{\text{cost price}}\times 100$
Hence substituting the values we get, $10=\dfrac{x-20000}{x}\times 100$
Now simplifying the above equation we get,
$\begin{align}
  & \Rightarrow 10x=\left( x-20000 \right)100 \\
 & \Rightarrow x=\left( x-20000 \right)10 \\
 & \Rightarrow x=\left( 10x-200000 \right) \\
 & \Rightarrow 9x=200000 \\
 & \Rightarrow x=22,222.22 \\
\end{align}$
Hence the cost price of VCR is 22,222.22.
Hence the loss is 22,222 – 20,000 = 2,222.22
Now let us consider the transaction of TV.
The cost price of the TV be x Rs. The selling price of TV is 20,000.
Now we know that profit = 20,000 – x.
Now the profit percentage is given by the formula $\dfrac{\text{profit}}{\text{cost price}}\times 100$
Hence substituting the values in the above equation we get, $\dfrac{20,000-x}{x}=5$
Now simplifying the above equation we get,
$\begin{align}
  & \Rightarrow \left( 20000-x \right)\times 100=5x \\
 & \Rightarrow \left( 20000-x \right)\times 20=x \\
 & \Rightarrow 400000-20x=x \\
 & \Rightarrow 400000=21x \\
 & \Rightarrow x=19047.61 \\
\end{align}$
Hence the cost price of TV is 19,047.61.
Hence the profit is 20,000 – 19,047 = 952.38.
Hence the profit is 952.38 and the loss is 2,222.22
Hence there was a loss of 2,222.22 – 952.38.
Hence the total loss was 1269.83.

Note: Note that the overall loss percentage is not the addition or subtraction of profit and loss percentage. Hence we have to consider both the cases separately to find profit and loss respectively and calculate the total profit or loss accordingly.