Question

A fruit seller purchased 50 Kg of mangoes at the rate of Rs.22 per Kg. He sold some of the mangoes at the rate of Rs.30 per Kg and the rest at the rate of Rs.20 per kg. If he incurred a $25\%$ profit overall, the amount of mangoes sold at the rate of Rs. 20 per kg is
(a) 12.5 kg
(b) 37.5 kg
(c) 25 kg
(d) 20.5 kg

Answer 1

Hint: First, we should find the cost price(CP) of the 50 kg mangoes. Then, we have to find the selling price of the 50 kg mangoes by increasing the cost price value by $25\%$ by using the formula $P\%=\dfrac{SP-CP}{CP}\times 100$. Then, let the mangoes be sold at Rs. 30 per kg be x. Then, we get that the mangoes can be sold at Rs. 20 per kg be 50-x. Now, by using these two conditions, we get the value of the amount of mangoes sold at the rate of Rs. 20 per kg.

Complete step-by-step solution:
In this question, we are supposed to find the amount of mangoes sold at the rate of Rs. $20$ per kg.
Now, In the question it is clearly mentioned that mangoes are purchased at the rate of Rs. $22$ per kg for the $50$ kg mangoes.
So, the cost price(CP) of the $50 kg$ mangoes is:
$50\times 22=1100$
So, the cost price(CP) of the $50$ kg mangoes is Rs. $1100$.
Then, it is given that a $25\%$ profit is made over the cost price by selling it at two different rates.
So, the Selling Price(SP) of the 50 kg mangoes, we use the formula of profit percentage as:
$P%=\dfrac{SP-CP}{CP}\times 100$
Now, substitute the value of profit percent as $25\%$ and CP as $1100$, then:
$\begin{align}
  & 25=\dfrac{SP-1100}{1100}\times 100 \\
 & \Rightarrow 25=\dfrac{SP-1100}{11} \\
 & \Rightarrow 275=SP-1100 \\
 & \Rightarrow SP=1375 \\
\end{align}$
So, the selling price(CP) of the $50$ kg mangoes is Rs. $1375$.
Now, let the mangoes be sold at Rs. $30$ per kg be $x$.
So, according to the above assumption, we get that the mangoes sold at Rs. $20$ per kg be 50-x.
Now, by using the above conditions, we get the expression as:
$30\times x+20\left( 50-x \right)=1375$
Now, solve the above expression to get value of x as:
$\begin{align}
  & 30x+1000-20x=1375 \\
 & \Rightarrow 30x-20x=1375-1000 \\
 & \Rightarrow 10x=375 \\
 & \Rightarrow x=\dfrac{375}{10} \\
 & \Rightarrow x=37.5 \\
\end{align}$
So, it gives the value of kilogram sold at Rs. $30$ per kg.
Now, to get the value of kilogram sold at Rs. $20$ per kg is given by:
$\begin{align}
  & 50-x=50-37.5 \\
 & \Rightarrow 12.5 \\
\end{align}$
So, the amount of mangoes sold at the rate of Rs. $20$ per kg is $12.5$ kg.
Hence, option (a) is correct.

Note: In these types of the question, there is no fixed approach to solve as we can also assume that the mangoes be sold at Rs. 20 per kg be x and subsequently the mangoes sold at Rs. 30 will become 50-x. Then, due to which the expression to get the value of x also changes as:
$30\times \left( 50-x \right)+20\times x=1375$
But, it also gives the amount of mangoes sold at the rate of Rs. 20 per kg is 12.5 kg.