Question

Padam purchased 30 kg of rice at the rate of 17.50 kg and another 30 kg of rice at a certain rate. He mixed the two and sold the entire quantity at the rate of 18.60 per kg and made 20% overall profit. At what price per kg did he purchase the other lot of 30 kg rice?
(A) Rs.12.50
(B) Rs.13.50
(C) Rs.14.50
(D) Rs.15.50

Answer 1

Hint: In the given problem, we have to find the price of the rice. Thus, we will use the cost price - selling price formula to get the solution. We start solving the problem by taking the price as $\text{Rs}.x$. Then, we will find the cost price and the selling price of 60 kg rice. In the last, we will find the profit percentage, using the formula, $\dfrac{\text{selling price - cost price}}{\text{cost price}}\times 100=\text{profit}$. Then, we will make the necessary calculations to get the value of x as our required solution for the problem.

Complete step by step answer:
According to the problem, we have to find the value of the price of rice. Thus, we will use the cost price - selling price formula to get the solution.
Let us first take the price of rice as equal to $\text{Rs}.x\ldots \ldots \ldots \left( 1 \right)$
So, the cost price of 60 kg rice is the sum of rice purchased the first time and the second time, thus we get,
$\begin{align}
  & \text{Rs}.\left( 30\times 17.50+30\times x \right) \\
 & \Rightarrow \text{Rs}.\left( 525+30x \right)\ldots \ldots \ldots \left( 2 \right) \\
\end{align}$
Similarly, we will find the selling price of both the times. So, we get,
$\begin{align}
  & \text{Rs}.\left( 60\times 18.60 \right) \\
 & =\text{Rs}.1116\ldots \ldots \ldots \left( 3 \right) \\
\end{align}$
Now, we know that the profit percentage is equal to 20% and its formula is given as,$\dfrac{\text{selling price - cost price}}{\text{cost price}}\times 100$. Thus, we will substitute the value of equation (2) and (3) in the given formula and we get,
$20=\dfrac{1116-\left( 525+30x \right)}{525+30x}\times 100$
On further solving the above equation, we get,
\[20=\dfrac{1116-525-30x}{525+30x}\times 100\]
Now, we will divide 100 on both sides in the above equation. So, we get,
$\begin{align}
  & \dfrac{20}{100}=\dfrac{591-30x}{525+30x}\times \dfrac{100}{100} \\
 & \Rightarrow \dfrac{1}{5}=\dfrac{591-30x}{525+30x} \\
\end{align}$
Now, we will cross multiply both sides in the above equation. So, we get,
$\begin{align}
  & 525+30x=\left( 591-30x \right)\times 5 \\
 & \Rightarrow 525+30x=2955-150x \\
\end{align}$
Now, we will add $150x$ and subtract 525 on both sides in the above equation, and we get,
$525+30x+150x-525=2955-150x+150x-525$
As we know the same terms with opposite signs cancel out each other, thus we get,
$180x=2430$
Now we will divide 180 on both sides, and we get,
$\dfrac{180x}{180}=\dfrac{2430}{180}$
Therefore, we get,
$x=\text{Rs}.13.50$

So, the correct answer is “Option B”.

Note: While solving this problem, do mention all the steps properly to avoid errors. Mention all the formula and standard units carefully to get an accurate answer. We should note that if selling price is greater than cost price then we will have profit and if cost price is greater than selling price then will have loss.