Question

Mukesh purchased $40\text{ kg}$ of wheat at $\text{Rs}\text{. }12.50$ per kg and $25\text{ kg}$ of wheat at $\text{Rs}\text{. }15.10$ per kg. He mixed the two qualities of wheat for selling. At what rate should it be sold to gain $10\%$ ?
A. $\text{Rs}\text{. }13.25$
B. $\text{Rs}\text{. }13.50$
C. $\text{Rs}\text{. }14.75$
D. $\text{Rs}\text{. }14.85$

Answer 1

Hint: In this problem we need to find the selling price of the wheat to get the gain of $10\%$. First we will calculate the cost price of the material. We have given that he purchased $40\text{ kg}$ of wheat at $\text{Rs}\text{. }12.50$ per kg and $25\text{ kg}$ of wheat at $\text{Rs}\text{. }15.10$ per kg. So we will calculate the total cost price by adding the product of $40\text{ kg}$, $\text{Rs}\text{. }12.50$ with $25\text{ kg}$, $\text{Rs}\text{. }15.10$. After having the cost price of the material we will calculate the amount which is $10\%$ of cost price by multiplying both of them. To get the final selling price add the calculated $10\%$amount to the cost price. Now we will divide the final cost price with the total weight of the material to the required result.

Complete step by step answer:
Given that, Mukesh purchased $40\text{ kg}$ of wheat at $\text{Rs}\text{. }12.50$ per kg and $25\text{ kg}$ of wheat at $\text{Rs}\text{. }15.10$ per kg.
He mixed the two quantities, then the total weight of the material will become $40\text{ kg}+25\text{ kg}=65\text{ kg}$ .
Total cost price of the material is given by
$\begin{align}
  & \text{cost price}=40\left( 12.50 \right)+25\left( 15.10 \right) \\
 & \Rightarrow \text{cost price}=500+377.5 \\
 & \Rightarrow \text{cost price}=877.5 \\
\end{align}$
Now the $10\%$ of the above cost price is calculated as
$\begin{align}
  & 10\%\text{ of }877.5=\dfrac{10}{100}\times 877.5 \\
 & \Rightarrow 10\%\text{ of }877.5=87.75 \\
\end{align}$
So the final selling price will become as the sum of $10\%$of the cost price with cost price, then we will get
$\begin{align}
  & \text{selling price}=877.5+87.75 \\
 & \Rightarrow \text{selling price}=965.25 \\
\end{align}$
Now the cost per one kg is given by dividing the above calculated selling price with the total weight of the material which is $65\ \text{kg}$ , then we will get
$\begin{align}
  & \text{cost per kg}=\dfrac{965.25}{65} \\
 & \Rightarrow \text{cost per kg}=14.85 \\
\end{align}$

Hence Mukesh has to sell the wheat at $\text{Rs}\text{. }14.85$ per kg to gain $10\%$.

So, the correct answer is “Option D”.

Note: In this problem we can also directly calculate the final selling price by multiplying $\dfrac{110}{100}$ with cost price which gives
$\begin{align}
  & \text{final selling price}=877.5\times \dfrac{110}{100} \\
 & \Rightarrow \text{final selling price}=965.25 \\
\end{align}$
Here we have got the same value in a single step, so we can use any one of these methods.