Question

The difference in prices when a commodity at a profit of 4% and at a profit of 6% is Rs 3. Find the selling prices of the commodity in both the cases.

Answer 1

Hint – In this question let the market price of the commodity be x Rs, and the selling prices price of the commodity be ${y_1}$ Rs and ${y_2}$ Rs for case one and case two respectively. Profit percentage can be calculated for both the cases as $\dfrac{{{y_1} - x}}{x} \times 100$ and $\dfrac{{{y_2} - x}}{x} \times 100$, use the equations to formulate equations and get the value of variables.
Complete step-by-step answer:
Let the market price of the commodity be x Rs.
And the selling price of the commodity will be ${y_1}$ Rs. in the first case and ${y_2}$ Rs. in the second case.
As there is a profit, the selling price must be greater than the market price.
As profit percentage is the ratio of difference of selling price and market price to market price multiplied by hundred.
Now in the first case it earns a profit of 4%.
$ \Rightarrow 4 = \dfrac{{{y_1} - x}}{x} \times 100$................ (1)
And in the second case it earns a profit of 6%.
$ \Rightarrow 6 = \dfrac{{{y_2} - x}}{x} \times 100$................. (2)
Now it is given that the difference in prices when the commodity is sold at a profit of 4% and at a profit of 6% is Rs. 3.
As the gain is higher in the second case, so the selling price in the second case must be higher.
$ \Rightarrow {y_2} - {y_1} = 3$
$ \Rightarrow {y_2} = 3 + {y_1}$............... (3)
Now substitute this value in equation (2) we have,
$ \Rightarrow 6 = \dfrac{{3 + {y_1} - x}}{x} \times 100$
Now from equation (1)
${y_1} - x = \dfrac{{4x}}{{100}}$ so substitute this value in above equation we have,
$ \Rightarrow 6 = \dfrac{{3 + \dfrac{{4x}}{{100}}}}{x} \times 100$
Now simplify this equation we have,
$ \Rightarrow 6 = \dfrac{{300 + 4x}}{x}$
$ \Rightarrow 6x = 300 + 4x$
$ \Rightarrow x = \dfrac{{300}}{2} = 150$ Rs.
Now substitute this value in equation (1) we have,
$ \Rightarrow 4 = \dfrac{{{y_1} - 150}}{{150}} \times 100$
$ \Rightarrow 600 = \left( {{y_1} - 150} \right)100$
$ \Rightarrow {y_1} = 150 + 6 = 156$Rs.
Now from equation (3) we have,
$ \Rightarrow {y_2} = 3 + 156 = 159$ Rs.
So the selling price of the commodity is Rs. 156 and Rs. 159 in both the cases.
So this is the required answer.

Note – A seller experiences a profit if and only if the selling price of that commodity is greater than the cost price, however it is exactly opposite in case of loss, in this case the cost price for the seller is much greater as compared to the cost price of the item. Here ${y_1}{\text{ and }}{{\text{y}}_2}$ are the selling prices thus profit is taken by the difference of cost price which is x and the selling price, thus percentage is taken out by dividing this expression with the cost price and multiplication with 100.