Question

A merchant on selling rice earns a profit of Rs. 10 per bag of basmati rice sold and a loss of Rs. 5 per bag of non-basmati rice.

(i) He sells $3,000$ bags of basmati rice and $5,000$ bags of non-basmati rice in a month. What is his profit or loss in a month

(ii) What is the number of basmati rice bags he must sell to have neither profit nor loss if the number of bags of non-basmati rice sold is $6,400$

A. $5000,3400$
B. $5000,3200$
C. $3500,5500$
D. $5000,3550$

Answer 1

Hint: For part (i) to solve we simply calculate the profit or loss on a given number of bags by multiplying the profit/loss per bag of respective rice, as we have been given the profit and loss of per bag. Now, to get the monthly profit of the merchant, deduct the obtained loss from profit. For part (ii), first, we assume the number of bags of basmati rice to be $x$, then we calculate the total profit and total loss by multiplying the respective number of bags and profit/loss per bag. Then, we will equate these two quantities to get the value of x.

Complete step by step solution:
We have given that a merchant earns a profit of Rs. 10 per bag of basmati rice sold on selling price and a loss of Rs. 5 per bag of non-basmati rice.
Now we solve the part (i)
We have to calculate the profit or loss in a month if a merchant sells $3,000$ bags of basmati rice and $5,000$ bags of non-basmati rice.
First, we have to calculate the profit earned by him on $3,000$ bags of basmati rice as given a profit of Rs. 10 per bag.
So, multiplying the number of bags and profit per bag, we get
Profit = Rs. $3000\times 10=30,000$
Now, we calculate the loss on $5,000$ bags of non-basmati rice as given a loss of Rs. 5 per bag.
So, multiplying the number of bags and loss per bag, we get
Loss = Rs. $5000\times 5=25000$
Here, we observe that the profit he earned is greater than the loss. So to calculate the net profit we subtract the loss from the profit.
We get net profit $=30000-25000=\text{ Rs}\text{. }5000$
A merchant earns a profit of $\text{Rs}\text{. }5000$ in a month.
Now, we solve part (ii)
We have to find the number of basmati rice bags he must sell to have neither profit nor loss.
We have given that the number of bags of non-basmati rice sold is $6,400$. Let us assume that the number of bags of basmati rice sold to be $x$.
If a merchant neither earns profit nor loss, then we have to equate both profit and loss he earns.
So, we will multiply the number of bags and profit per bag and also multiply the number of bags and loss per bag, and equate them as below,
$\begin{align}
  & 10\times x=6400\times 5 \\
 & 10x=32000 \\
 & x=\left( \dfrac{32000}{10} \right) \\
 & x=3200 \\
\end{align}$
It means if a merchant sells $3,200$ number of bags of basmati rice and $6,400$ number of bags of non-basmati rice, he neither earns profit nor loss.
So, the correct answer is option B.

Note: The point to note is that the general formula used to calculate the selling price is $\text{SP=CP+Profit margin}$. But in this question, we have given that the profit is earned on selling. So we calculate directly by multiplying the number of bags with profit earned per bag. Similarly, we calculate the loss. Students must be aware of and multiply the corresponding values to get the right answer. They can first note down the details as below to avoid confusion and reading the question multiple times.
Basmati Rice: Profit per bag = Rs. 10, number of bags = 3000 for part (i) and x for part (ii)
Non-Basmati Rice: Loss per bag = Rs. 5, number of bags = 5000 for part (i) and 6400 for part (ii)