Question

A dealer earned a profit of 5% by selling radio for ₹ 714. Find the cost price of the radio.

Answer 1

Hint: As we know that the Cost Price (C.P) means the amount which is paid by the seller to acquire that product and Selling Price (S.P) is the money that is finally received by the seller after selling that same product to any customer.
If the S.P is more than the C.P then there will be profit and if C.P is more than the S.P then there will be a loss for the seller.
Hence, Profit % is the percent of the profit gained by the seller and loss % is the percent of loss suffered by the seller.
Profit and loss for any product are given by:
$Profit = S.P - C.P$
$Loss = C.P - S.P$
Now Profit and Loss percentage can be calculated by:
\[Profit\% = \dfrac{{Profit}}{{C.P}} \times 100\]
\[Loss\% = \dfrac{{Loss}}{{C.P}} \times 100\]

Complete step-by-step answer:
Given,
\[\begin{gathered}
  Profit = 5\% \\
  S.P{\text{ }} = \;Rs.714 \\
    \\
\end{gathered} \]
Let us denote Profit by ‘P’
We know that
\[Profit\% = \dfrac{{Profit}}{{C.P}} \times 100\]
Then,
\[C.P = \dfrac{{Profit}}{{Profit\% }} \times 100\]
By putting the value of Profit % we get
\[C.P = \dfrac{P}{5} \times 100\]
i.e. \[C.P{\text{ }} = {\text{ }}20P\] eqn (i)
Also,
\[Profit{\text{ }} = {\text{ }}S.P{\text{ }} - {\text{ }}C.P\]
By using eqn(i) and putting value of S.P, we get
\[\begin{array}{*{20}{l}}
  {21P{\text{ }} = {\text{ }}714} \\
  {P = 34}
\end{array}\]

Using the value of P in equation (i), we get
\[C.P = 20 \times 34\]
Hence,
\[C.P = \;Rs.{\text{ }}680\]
Note: Cost Price can also be calculated by simply using the formula given below:
\[C.P = \dfrac{{100}}{{100 + P\% }} \times S.P\]
Never Confuse C.P with S.P the C.P means the cost price and S.P means selling price.
And there would be Profit only if \[S.P{\text{ }} > {\text{ }}C.P\]