Question

The marked price M.P of a camera is $\dfrac{3}{2}$ of the C.P and S.P is $\dfrac{9}{{10}}$ of the M.P. Find the percentage of profit or loss.
$
  (a){\text{ 25% profit}} \\
  (b){\text{ 35% profit}} \\
  (c){\text{ 33}}{\text{.33% loss}} \\
  (d){\text{ none of these}} \\
 $

Answer 1

Hint – In this question let the cost price (C.P), marked price (M.P) and the selling price (S.P) of the camera be x, y and z respectively. Use the relations given in question to formulate equations involving these variables. Then use the concept that profit is simply the subtraction of selling price and the cost price and loss is the subtraction of cost price and the selling price (in case loss is there) . After this percentage can be evaluated.

Complete step-by-step answer:
Let the cost price (C.P) of the camera = x
Market price (M.P) of the camera = y
And the selling price (S.P) of the camera = z.
Now it is given that M.P of the camera is (3/2) of the C.P.
So construct the linear equation according to this information we have,
$ \Rightarrow y = \dfrac{3}{2}x$.................... (1)
Now it is given that S.P of the camera is (9/10) of the M.P.
So construct the linear equation according to this information we have,
$ \Rightarrow z = \dfrac{9}{{10}}y$.................... (2)
Now from equation (1) substitute the value of y in equation (2) we have,
$ \Rightarrow z = \dfrac{9}{{10}}\left( {\dfrac{3}{2}x} \right) = \dfrac{{27}}{{20}}x$
Now as we see S.P is greater than the C.P so there is a profit.
Now as we know profit is the difference between selling price and cost price.
Therefore profit (P) = S.P – C.P
                                   $ = z - x$
                                   $ = \dfrac{{27}}{{20}}x - x = \dfrac{{27 - 20}}{{20}}x = \dfrac{7}{{20}}x$
Now %profit is the ratio of profit to cost price multiplied by 100.
Therefore %profit $ = \dfrac{P}{x} \times 100$
                                 $ = \dfrac{{\dfrac{7}{{20}}x}}{x} \times 100 = 35$ %
So there is 35% of profit.
So this is the required answer.
Hence option (B) is correct.

Note – Here we have computed profit and not loss because the value of subtraction of selling price and cost price will come out to be positive as Profit = $z - x$, and z is $\dfrac{{27}}{{20}}$ of x and cost price was x, so simply the selling price was larger, if this would not have been the case then there would be a loss and the percentage of loss would have been evaluated.