Certainly! Let's tackle this problem step by step.
### Part i: Calculating Monthly Profit or Loss
First, we need to determine the total profit from selling wheat and the total loss from selling rice.
1. Calculate the total profit from wheat:
- Profit per bag of wheat: 12
- Number of wheat bags sold: 1500
- Total profit from wheat = [tex]\( 12 \times 1500 \)[/tex]
2. Calculate the total loss from rice:
- Loss per bag of rice: 8
- Number of rice bags sold: 2050
- Total loss from rice = [tex]\( 8 \times 2050 \)[/tex]
3. Determine the net profit or loss:
- Net profit or loss = Total profit from wheat - Total loss from rice
Let's compute these values.
1. Total profit from wheat:
[tex]\[
\text{Total profit from wheat} = 12 \times 1500 = 18000
\][/tex]
2. Total loss from rice:
[tex]\[
\text{Total loss from rice} = 8 \times 2050 = 16400
\][/tex]
3. Net profit or loss:
[tex]\[
\text{Net profit or loss} = 18000 - 16400 = 1600
\][/tex]
Therefore, the wholesaler makes a net profit of 1600 in the month.
### Part ii: Number of Wheat Bags to Sell for No Profit or Loss
For no profit or loss, the total profit from selling wheat should equal the total loss from selling rice.
1. Define the number of wheat bags to be sold to achieve neither profit nor loss:
- Let [tex]\( x \)[/tex] be the number of wheat bags that need to be sold.
- We know that the total loss from rice is given, and we need to balance it with an equal amount of profit from wheat.
2. Formulate the equation:
- Total profit from wheat = Total loss from rice
- Profit per bag of wheat [tex]\(\times x = \text{Loss per bag of rice} \times \text{Number of rice bags sold}\)[/tex]
- [tex]\( 12 \times x = 8 \times 2400 \)[/tex]
3. Solve for [tex]\( x \)[/tex]:
[tex]\[
12 \times x = 8 \times 2400
\][/tex]
[tex]\[
12x = 19200
\][/tex]
[tex]\[
x = \frac{19200}{12}
\][/tex]
[tex]\[
x = 1600
\][/tex]
Therefore, the wholesaler must sell 1600 bags of wheat to have neither profit nor loss if he sells 2400 bags of rice.
In summary:
- The wholesaler makes a net profit of 1600 for selling 1500 bags of wheat and 2050 bags of rice in a month.
- To achieve neither profit nor loss, he must sell 1600 bags of wheat if he sells 2400 bags of rice.
