QUESTION

# A shopkeeper sells markers at the rate of Rs.35 each and earns a commission of 10%. He also sells gel pens at the rate of Rs.65 each and earns a commission of 20%. How much amount (in rupees) of commission will he earn in 2 weeks, if he sells 12 markers and 8 gel pens a day?

Hint: In this question, we need to calculate the cost of marker and gel pen by using the given cost of them along with commission. Then calculate the profit earned on each of them and then calculate profit earned on all of them together.

Let us assume the cost of the marker as x.

Cost of gel pen as y.

From the question as given the cost of marker with 10% commission we can write the equation as follows:

According to the percentage formula x% of y can be written as

$\dfrac{x}{100}\times y$

$\Rightarrow x+\dfrac{10}{100}\times x=35$

Now, on further simplification we get,

\begin{align} & \Rightarrow x+\dfrac{1}{10}\times x=35 \\ & \Rightarrow \dfrac{11}{10}x=35 \\ \end{align}

Now, as we know that 10% of x is the profit on x we get,

$\therefore \dfrac{x}{10}=Rs.\dfrac{35}{11}$

Similarly, now on considering the gel pen we get,

From the question as given the cost of gel pen with 20% commission we can write the equation as follows:

$\Rightarrow y+\dfrac{20}{100}\times y=65$

Now, on further simplification we get,

\begin{align} & \Rightarrow y+\dfrac{1}{5}\times y=65 \\ & \Rightarrow \dfrac{6}{5}y=65 \\ \end{align}

Now, as we know that 20% of y is the profit on y we get,

$\therefore \dfrac{y}{5}=Rs.\dfrac{65}{6}$

Total number of markers sold in 2 weeks will be:

\begin{align} & \Rightarrow 14\times 12 \\ & \Rightarrow 168 \\ \end{align}

Now, the profit earned on selling these markers is:

\begin{align} & \Rightarrow \dfrac{35}{11}\times 168 \\ & \Rightarrow Rs.\dfrac{5880}{11} \\ \end{align}

Total number of gel pens sold in 2 weeks will be:

\begin{align} & \Rightarrow 14\times 8 \\ & \Rightarrow 112 \\ \end{align}

Now, the profit earned on selling gel pens is:

\begin{align} & \Rightarrow \dfrac{65}{6}\times 112 \\ & \Rightarrow Rs.\dfrac{3640}{3} \\ \end{align}

Total profit earned in 2 weeks is:

\begin{align} & \Rightarrow \dfrac{5880}{11}+\dfrac{3640}{3} \\ & \Rightarrow Rs.1747.88 \\ \end{align}

Note: Instead of calculating the profits separately and adding them we can directly calculate it by considering the equation by adding the selling prices of both of them and then equating to the additional terms. But this will be a lengthy process and a bit confusing.
While calculating the values it is important to calculate the profit earned on each marker and gel pen from the equations which is the only possible way to calculate the total profit earned at the end of 2 weeks.
We need to be careful while adding, subtracting and rearranging the terms because neglecting any of the terms changes the answer accordingly.