Question

A merchant selling rice earns profit Rs 10 per bag of basmati rice sold and a loss of Rs 5 per bag of non-basmati rice.
What are the number of basmati rice bags he must sell to have neither profit nor loss, if the number of bags of non-basmati rice bags sold are 6400?

Answer 1

Hint: Loss attained by selling a product = - (Profit attained by selling a product). We should remember this point. In this question, the sum of profit obtained by selling basmati bags and loss obtained by selling non-basmati is equal to zero.

Complete step-by-step solution -
Before solving the question, we should write each and every information given. In the question, it was given that a merchant selling rice earns profit Rs 10 per bag of basmati rice sold and a loss of Rs 5 per bag of non-basmati rice.
Profit obtained by selling a one bag of basmati rice = Rs 10
Loss obtained by selling a one bag of non-basmati rice = Rs 5
In the question, we are given that the number of non-basmati rice bags sold =6400.
Let Loss obtained by selling 6400 non-basmati bags = x.
\[\begin{align}
  & 1\to 5 \\
 & 6400\to x \\
\end{align}\]
By criss-cross method,
\[\begin{align}
  & 1.x=5(6400) \\
 & \Rightarrow x=32000....(1) \\
\end{align}\]
Therefore, the loss obtained by selling 6400 non-basmati rice bags = 32000.
Let us assume the number of basmati bags sold = y.
Then, the profit obtained by selling y basmati rice bags = 10y.
From the question, it is given that the merchant should neither gain profit nor loss. The resultant amount obtained after selling 6400 non-basmati rice bags and y basmati rice bags is zero.
So, loss obtained by selling 6400 non-basmati rice bags = profit obtained by selling 10y basmati bags.
 \[\begin{align}
  & \Rightarrow 6400=10y \\
 & \Rightarrow y=640.....(2) \\
\end{align}\]
Hence, the number of basmati rice bags sold by the merchant = 640.

Note: If the difference between selling price and cost price is greater than zero, then the difference is said to be profit. In the same way, if the difference between selling price and cost price is less than zero, then the difference is said to be loss. Based on the cost price and selling price, profit and loss are decided.