Question

On selling a watch for Rs. 11,400, a shopkeeper loses 5 %. For how much did he purchase it?

Answer 1

Hint: To solve this question, we will use the formula of loss percent which is given as \[\text{Loss Percent}=\dfrac{Loss}{CP}\times 100\] where \[Loss=CP-SP\] and CP is the cost price and SP is the selling price. After substituting all the given values, we will get the CP of the watch.

Complete step-by-step solution
We are given that the selling price of the watch is Rs. 11,400.
\[\Rightarrow SP\left( \text{Selling Price} \right)=Rs.11400\]
We are given that the shopkeeper loses 5 %.
\[\Rightarrow \text{Loss Percent}=5\text{ Percent}\]
The formula of loss percentage is given by
\[\text{Loss Percent}=\dfrac{Loss}{CP}\times 100\]
where Loss = CP – SP and CP are the cost price and SP is the selling price.
\[\Rightarrow \text{Loss Percent}=\dfrac{Loss}{CP}\times 100\]
Substituting, Loss = CP – SP, we get,
\[\Rightarrow \text{Loss Percent}=\dfrac{CP-SP}{CP}\times 100\]
We are given that the SP of the watch is 11400 and loss % = 5 %. Substituting the values of loss percent and SP in the above equation, we get,
\[\Rightarrow \text{Loss Percent}=\dfrac{CP-SP}{CP}\times 100\]
\[\Rightarrow 5\text{ Percent}=\dfrac{CP-11400}{CP}\times 100\]
5 percent is nothing but \[\dfrac{5}{100}.\]
\[\Rightarrow \dfrac{5}{100}=\dfrac{CP-11400}{CP}\times 100\]
Dividing the terms on the RHS, we have
\[\Rightarrow \dfrac{5}{100}=\left( 1-\dfrac{11400}{CP} \right)\times 100\]
Taking 100 from RHS to the LHS, we have
\[\Rightarrow \dfrac{5}{10000}=1-\dfrac{11400}{CP}\]
Now, we will keep the term with CP on the RHS and then we have
\[\Rightarrow 1-\dfrac{5}{10000}=\dfrac{11400}{CP}\]
Taking the LCM of terms, we have
\[\Rightarrow \dfrac{10000-5}{10000}=\dfrac{11400}{CP}\]
Performing cross-multiplication, we have
\[\Rightarrow CP=\dfrac{11400\times 10000}{9995}\]
\[\Rightarrow CP=\dfrac{11400}{0.9995}\]
\[\Rightarrow CP=11,406\]
Therefore, the cost price of the watch is Rs.11406. So he did purchase it at a cost price (CP) of Rs. 11,406.

Note: Whenever the CP is greater than the SP, CP > SP, there is a loss here. Observe that CP = 11406 and SP is 11400. So, 11406 > 11400. Hence, it was a loss. If CP < SP, then in that case, when the profit occurs, \[\text{Profit Percent}=\dfrac{\text{Profit}}{CP}\times 100.\]