Question

Sita sells a dining set to Neeta for \[{\text{Rs 6000}}\] and gains \[20\% \]. For how much should she sell it to increase her profit by another \[5\% \]?

Answer 1

Hint: To solve it we will first consider the original price of the dining set to be \[x\]. Then we will calculate \[20\% \] of \[x\] and add to \[x\] and equate the result to \[{\text{Rs 6000}}\]. Then from this equation we will find the value of the original price. Further we will calculate \[25\% \] of the original price because she has to get another $5\%$ profit and add to the original price to get the required answer.

Complete step by step answer:
Let the original price of the dining set to be \[x\].
Now a gain of \[20\% \], on it results in its selling price of \[{\text{Rs 6000}}\]. So, from this we set an equation as;
\[x + 20\% {\text{ of }}x = 6000\]
So, we get,
\[ \Rightarrow x + \dfrac{{20}}{{100}}x = 6000\]
On dividing we get;
\[ \Rightarrow x + \dfrac{1}{5}x = 6000\]
Solving by taking the LCM we get;
\[ \Rightarrow \dfrac{6}{5}x = 6000\]
\[ \Rightarrow x = 6000 \times \dfrac{5}{6}\]
On calculating we get;
\[ \Rightarrow x = 5000\]
So, the original price of the dining set is \[{\text{Rs }}5000\].
Now if we will calculate \[25\% \] of it and then add to it. So, we get,
\[5000 + 5000 \times \dfrac{{25}}{{100}}\]
On solving we get;
\[5000 + 1250 = {\text{Rs }}6250\]

Hence, in order to gain \[5\% \] extra she should sell it at \[{\text{Rs }}6250\].

Note: Profit or gain means that the selling price is more than the cost price and loss means that the cost price is more than the selling price. One point to note here is that, both the profit and loss percent are calculated on the cost price and not on the selling price.Another term we found here is discount. Discount is the difference between the marked price and the selling price.