Question

Mechanic Raj purchased a motorcycle for Rs. 20,000 and sold it at 5 % loss. Its selling price is
A. Rs. \[\dfrac{5}{{100}} \times 20,000\]
B. Rs. \[\dfrac{{95}}{{100}} \times 20,000\]
C. Rs. \[\dfrac{{105}}{{100}} \times 20,000\]
D. Rs. \[\dfrac{{100}}{{95}} \times 20,000\]

Answer 1

Hint: Here this question is related to loss and profit. In this they have mentioned about the cost price and the loss percentage. By using the formula of loss percentage, we can find the selling price. Hence, we obtain the required solution for the question. The solution is present in the above options.

Complete step-by-step solution:
By data we have
The cost price of the motorcycle is given by \[C.P = 20,000\]
The loss percentage is equal t0 5% and it is given by \[loss\% = 5\% \]
Since they mentioned loss percentage the cost price is more than the selling price and the cost price is 20,000
The formula for the selling price when the loss percentage is given by
\[S.P = C.P\left[ {1 - \dfrac{{loss\% }}{{100}}} \right]\]
Where C.P means cost price and S.P means selling price.
The cost price of motorcycle is 20,000 and the loss in percentage is 5 %. Substituting these values in the formula we have
\[ \Rightarrow S.P = 20,000\left[ {1 - \dfrac{5}{{100}}} \right]\]
Taking LCM we have
\[ \Rightarrow S.P = 20,000\left[ {\dfrac{{100 - 5}}{{100}}} \right]\]
Therefore, on simplifying we get
\[ \Rightarrow S.P = 20,000\left[ {\dfrac{{95}}{{100}}} \right]\]
The above equation is written in the form of \[S.P = \dfrac{{95}}{{100}} \times 20,000\]

Hence the correct answer is option ‘B’.

Note: If the cost price is greater than the selling price then it is a loss. Otherwise, if the selling price is greater than cost price then it is gained. We can calculate the loss in percentage by Loss in percentage \[ = \dfrac{{C.P - S.P}}{{C.P}} \times 100\] and gain in percentage by gain in percentage \[ = \dfrac{{S.P - C.P}}{{C.P}} \times 100\]. The loss and gain depend on the cost price and selling price.