Question

The selling price of a sofa-set is \[\dfrac{4}{5}\] times of its cost price. Find the gain or the loss as percent.

Answer 1

Hint: Here, we will first assume the costing price and then find the selling price from the cost price. Then we will check if the costing price is greater than the selling price and find the gain or loss percentage using the formula \[{\text{Loss/Gain}}\% = \dfrac{{{\text{Loss/Gain}}}}{{{\text{C.P.}}}} \times 100\] , where C.P. is a cost price, from the given values.

Complete step-by-step solution
Let us assume that the cost price \[{\text{C.P.}}\] is \[x\].

It is given that the selling price of a sofa-set is \[\dfrac{4}{5}\] times of the cost price, \[x\].

We will now find the selling price \[{\text{S.P.}}\] of a sofa-set,

\[
  {\text{S.P.}} = \dfrac{4}{5} \times x \\
   = \dfrac{4}{5}x \\
\]

Thus, the selling price of a sofa-set is \[\dfrac{4}{5}x\].

Since \[x < \dfrac{4}{5}x\], the costing price is greater than the selling price, there is loss.

We know that loss is calculated by using the formula, \[{\text{Loss}} = {\text{C.P.}} - {\text{S.P.}}\], where C.P. is the cost price and S.P. is the selling price.

Subtracting the \[{\text{S.P.}}\] from \[{\text{C.P.}}\] to find the loss, we get

\[
  {\text{Loss}} = x - \dfrac{4}{5}x \\
   = \dfrac{{5x - 4x}}{5} \\
   = \dfrac{1}{5}x \\
\]

Since we know that the loss is \[\dfrac{x}{5}\], then the loss percentage is calculated using the formula, \[{\text{Loss}}\% = \dfrac{{{\text{Loss}}}}{{{\text{C.P.}}}} \times 100\], where C.P. is the cost price.

Substituting the values of Loss and C.P. in the above formula for loss percentage, we get

\[
  {\text{Loss}}\% = \dfrac{{\dfrac{x}{5}}}{x} \times 100 \\
   = \dfrac{1}{5} \times 100 \\
   = \dfrac{{100}}{5} \\
   = 20\% \\
\]

Thus, we get that a loss of \[20\% \] from a given sofa-set.

Note: In these types of questions, we first assume cost price as any variable and then the selling price. In this question, students should find out gain or loss by comparing between the selling price and the cost price. When the selling price is greater than the cost price, there is profit and when the cost price is greater than the selling price, there is loss. Then we will find the gain or loss percentage.