Question

A trader marks his goods 20%above the price. He then sells them at a discount of \[20\% \]. If the cost price is Rs.550, what are the gain or loss and the gain or loss percentage?

Answer 1

Hint: In this question we are going to calculate the gain or loss and the gain or loss percentage by finding first the marked price and then the discount and with the help of formula to find the selling price from the given data in the problem, and find whether the trader has profit or loss and finally we will find the profit or loss percentage using the percentage formula.

Formula used:
\[{{S}}{{.P = M}}{{.P - Discount}}\]
Where \[{{loss}}\% = 4\% \] S.P is the selling price of the good
M.P is the marked price of the good
For finding the gain or loss percentage we use the below formula,
\[{{gain}}\% = ({{gain}}/C.P) \times 100\]
\[{{loss}}\% = ({{loss}}/C.P) \times 100\]

Complete step by step solution:
First we have to calculate the marked price of the good
Since, we have given the cost price of the good that is Rs.550
And also in very first line it is given marked price is 20% above the cost price,
So we use the above relation to find the marked price,
So marked price= \[20\% \] more that the cost price
\[M.P = C.P + 20\% {{ of }}C.P\]
Now putting the value of cost price we get,
\[M.P = 550 + 20\% {{ of }}550\]
Solving above equation for marked price we get, writing % as 1/100
\[M.P = 550 + \dfrac{{20}}{{100}} \times 550\]
Multiplying 550 and 20 we get,
\[M.P = 550 + \dfrac{{11000}}{{100}}\]
Now, dividing 11000 by 100 we get the above equation as
\[M.P = 550 + 110\]
\[M.P = 660\]
So by adding we get the marked price as Rs.660 ------------------- [1]
Now, we will calculate the discount given on goods,
As given in the question discount is 20% off the marked price
So the above statement is written as,
\[{{Discount}} = 20\% {{ of }}M.P\]
Replacing % by 1/100 and putting the value of marked price from equation [1] we get
\[{{Discount}} = \dfrac{{20}}{{100}} \times 660\]
Now multiplying 20 and 660 we get,
\[{{Discount}} = \dfrac{{13200}}{{100}}\]
Now, dividing 132000 by 100 we get,
\[{{Discount}} = Rs.132\]-------------------- [2]
Now from above formula to find the selling price stated above we will find the selling price,
\[S.P = M.P - {{Discount}}\]
Putting the values of marked price and discount from equation [1] and equation [2] we get,
\[S.P = 660 - 132\]
Subtracting 132 from 660 we get,
\[S.P = Rs.528\] ------------------ [3]
From equation [1] and equation [2] we notice that selling price is less that the cost price that means there is a loss in goods
$S.P < C.P$
To find the loss in goods we use the below formula,
\[{{loss}} = C.P - S.P\]
Putting the values of cost price and selling price from equation [3] we get,
\[{{loss}} = 550 - 528\]
\[{{loss}} = Rs.22\]---------------- [4]
Now, we will find the loss percentage from the above stated formula we get,
\[{{loss}}\% = ({{loss}}/C.P) \times 100\]
Putting the value of loss and cost price from given problem and equation [4] we get,
\[{{loss}}\% = (22/550) \times 100\]
Dividing 22 by 550 we get,
\[{{loss}}\% = (0.04) \times 100\]
Now multiplying we get,
\[{{loss}}\% = 4\% \]

$\therefore$ Hence, the loss is Rs.22 and the loss percentage is 4%.

Note:
Here we should find the value of selling price and cost price and must compare both to find the loss or gain for the trader. For that we should carefully check the following identities that are, the trader faces loss if the cost price is greater than the selling price and gain if the cost price is less than the selling price.