Question

Deepak sold a study table for \[Rs.2231\] at a loss of \[3\% \] .At what price should he sell it so as to gain \[5\% \] .

Answer 1

Hint: To solve this question where they have asked the value of selling price at which he earns a gain of \[5\% \] , we will use the concepts of cost price, loss, profit and selling price .Using the formula of cost price we find the cost price substituting values of loss percentage and selling price. Then using the profit formula we get the value of profit earned .Finally we find the selling price substituting values of the cost price and profit value which is indeed the price at which he should sell to gain \[5\% \] .

Complete step by step answer:
Selling Price (SP): It is the amount at which a product is sold. It may be more than, equal to or less than the cost price of the product.
According to the above definition we can say \[SP = Rs.2231\] .
Loss Percent (\[L\% \]): It is the percentage of loss on the cost price.
Now we write \[L\% \] \[ = 3\% \]
Profit Percent (\[P\% \]): It is the percentage of profit on the cost price.
We say \[P\% \] \[ = 5\% \]
We can write cost price formula in terms of loss percentage and selling price as \[CP = \left[ {\dfrac{{100}}{{100 - L\% }}} \right] \times SP\]
Substituting the values of loss percentage \[L\% \]\[ = 3\% \] and \[SP = Rs.2231\] we get
\[CP = \left[ {\dfrac{{100}}{{100 - 3}}} \right] \times 2231\]
\[ \Rightarrow CP = 2300{\text{ / - }}\] , this is the cost price of the study table sold by Deepak.
We can write \[{\text{Profit% }} = \left( {\dfrac{{{\text{profit}}}}{{CP}}} \right) \times 100\]
As we know from the question \[{\text{Profit % }} = 5\% \]
\[5 = \left( {\dfrac{{{\text{profit}}}}{{2300}}} \right) \times 100\]
\[5 \times 23 = {\text{profit}}\]
\[ \Rightarrow {\text{profit}} = 115/{\text{ - }}\]
Now Deepak needs to sell the study table at \[SP\] so that he gains \[5\% \]
We write selling price \[{\text{SP}} = {\text{CP}} + {\text{Profit}}\]
\[ = 2300 + 115\]
\[ = 2415/ - \]
\[ \Rightarrow SP = 2415/ - \]
Therefore, Deepak needs to sell the study table at a price of \[ \Rightarrow SP = 2415/ - \] to gain \[5\% \] .

Note:
When we face such a type of problem, the key point is that we must have a good understanding about the concepts of selling price and cost price. We must be aware of the various formulas including the parameters like selling price, cost price, loss, profit, etc. By using the appropriate formula, the required solution can be obtained.