Question

Manish bought 1000 pencils for 3000 dollars and sold 200 dollars of these at a gain of \[ 5\%\]. At what gain percent he must sell the remaining pencils so as to gain \[15\%\] on the whole transaction?

Answer 1

Hint:
Here we have to find the gain percent. We will first find the cost price of the 200 pencils. Then we will find the profit earned on it. Again we will find the cost price of remaining pencils and then find the profit earned on the remaining pencil. We will further subtract the profit of 200 pencils from remaining pencils to find the required profit percent.

Formula used: We will use the formula \[{\rm{gain}} = \dfrac{{{\rm{gain}}\% \times {\rm{C}}{\rm{.P}}{\rm{.}}}}{{100}}\], where \[{\rm{C}}{\rm{.P}}{\rm{.}}\] is the cost price of the object.

Complete step by step solution:
It is given that the cost price of 1000 pencils is Rs 3000.
Therefore, cost price of one pencil \[ = \dfrac{{3000}}{{1000}} = {\rm{Rs}}3\]
Cost of 200 pencils \[ = 3 \times 200 = {\rm{Rs}}600\]
Manish sold 200 pencils at a gain percent of \[5\% \].
Now substituting in the formula \[{\rm{gain}} = \dfrac{{{\rm{gain}}\% \times {\rm{C}}{\rm{.P}}{\rm{.}}}}{{100}}\], we get
Therefore,
Profit earned on selling 200 pencils \[ = \dfrac{{5 \times 600}}{{100}} = Rs30\]
Selling price of 200 pencils\[ = {\rm{profit}} + {\rm{C}}{\rm{.P}}.\]
Putting the values of profit and C.P. in the above equation, we get
Selling price of 200 pencils\[ = 30 + 600 = {\rm{Rs}}630\]
Manish wants to make profit of \[15\% \] on the whole transaction.
Profit earned on whole transaction \[ = \dfrac{{15 \times 3000}}{{100}} = {\rm{Rs}}450\]
Profit on selling remaining pencils\[ = \] profit on whole transaction \[ - \] profit on 200 pencils
Profit on selling remaining pencils \[ = 450 - 30 = {\rm{Rs}}.420\]
As there are still 800 pencils left after selling 200 pencils, so we will calculate the cost price of the remaining pencil.
Cost price of the remaining pencils\[ = 800 \times 3 = {\rm{Rs}}2400\]
Profit made on the remaining pencils \[ = \]Cost price of the remaining pencils \[ \times \dfrac{{{\rm{gain}}\% }}{{100}}\]
Putting values of cost price of remaining pencils and its gain percent, we get
\[420 = 2400 \times \dfrac{{{\rm{gain}}\% }}{{100}}\]
Simplifying the terms, we get
\[{\rm{gain}}\% = \dfrac{{420 \times 100}}{{2400}}\% = 17.5\% \]

Hence, the required gain percent is \[17.5\% \].

Note:
We have calculated the profit earned on selling the given number of pencils. A profit or gain is defined as the extra money that we earn on selling any product whereas the loss is defined as the money that we lost on selling any product. If the selling price of the product is greater than the cost price of the product, then we make profit and vice-versa.