Question

A shopkeeper sold a TV set for RS 17940 with a discount of 8% and earned a profit of 19.6%. What would have been the percentage of profit earned if no discount was offered?
 (A) 24.8%
 (B) 25%
 (C) 30%
 (D) None of these

Answer 1

Hint: We are provided with S.P, the discount and the profit obtained, if we were asked to provide a discount the profit would have been even more than the profit obtained earlier. For finding the profit without discount we have to find the actual selling price mentioned on the T.v, which we will get from the discount. Then we will find the cost price from it and then the profit.
Complete step-by-step solution -
Let the marked price be Rs. X
Discount = 8%
∴ if the price be 100% then discount will be 100-8% i.e. 92%
\[\begin{gathered}
   \Rightarrow \dfrac{{92x}}{{100}} = Rs.17940 \\
   \Rightarrow x = \dfrac{{179400}}{{92}} = Rs.19500 \\
\end{gathered} \]
Profit = 19.6%
S.P = Rs. 17490
Using the formula of C.P,
\[C.P = \left( {\dfrac{{100}}{{100 + gain}}} \right) \times S.P\]
\[\begin{gathered}
   = \left( {\dfrac{{100}}{{100 + 19.6}}} \right) \times 17940 \\
   = Rs.15000 \\
\end{gathered} \]
If no discount was offered then
C.P =Rs 15000 and S.P= Rs 19500
Then profit = S.P – C.P
=19500-1500
=Rs. 4500
Now using the formula for profit% we get,
\[Profit\% = \left( {\dfrac{{profit}}{{C.P}}} \right) \times 100\]
=30%
Thus the correct option is ‘C’.
Note: For finding the Cost price we have to use the S.P for which the customer bought the Tv. And for finding the profit without a discount we have to Use the S.P or marked price on which the discount was offered, students sometimes make mistakes in this.