Question

A person by selling an article for Rs. 180 loses 10% In order to make a profit at which he must sell?
A) Rs. 210
B) Rs. 220
C) Rs. 200
D) Rs. 230

Answer 1

Hint: 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 loss for the seller.
Hence, Profit % is the percent of profit gained by the seller and loss % is percent of loss suffered by the seller.
Profit and loss for any product is given by:
$Profit = S.P - C.P$
$Loss = C.P - S.P$
Now Profit and Loss percentage can be calculated by using the formula given below:
\[Profit\% = \dfrac{{Profit}}{{C.P}} \times 100\]
\[Loss\% = \dfrac{{Loss}}{{C.P}} \times 100\]

Complete step-by-step answer:
Given,
Selling Price \[ = Rs.180\]
Loss % \[ = 10\% \]
Now as we know that Loss $ = C.P - S.P$ ----Eqn (i)
Also loss % \[ = \dfrac{{Loss}}{{C.P}} \times 100\]
Putting value of Loss % and Loss in the above equation we get,
\[\begin{gathered}
   \Rightarrow 10 = \dfrac{{C.P - S.P}}{{C.P}} \times 100 \\
   \Rightarrow \dfrac{{C.P}}{{10}} = C.P - 180 \\
\end{gathered} \]
That is, \[C.P = Rs.200\]
Now if profit % \[ = 10\% \]
And C.P \[ = Rs.200\];
Profit = \[\dfrac{{\Pr ofit\% \times C.P}}{{100}}\]
That is, Profit \[ = Rs.20\]
Hence the Selling Price to get a profit % of 10 % will be \[ = C.P + \Pr ofit\]
∴S.P \[ = Rs.220\]

Hence option (B) is the correct answer.

Note: Never Confuse C.P with S.P.
And there would be Profit only if \[S.P{\text{ }} > {\text{ }}C.P\]
And Cost Price can also be calculated by simply using the formula given below:
\[C.P = \dfrac{{100}}{{100 + P\% }} \times S.P\]