A part of monthly expenses of a family is constant and the remaining part varies with the price of wheat. When the rate of wheat is Rs. 250 a quintal, the total monthly expenses of the family are Rs. 1000, and when it is Rs. 240 a quintal, the total monthly expenses are Rs. 980. Find the total monthly expenses of the family, when the cost of wheat is Rs. 350 a quintal.

Answer

To solve the problem step by step, we will define the variables and set up the equations based on the information provided.

### Step 1: Define the Variables
Let:
- \( C \) = constant part of the monthly expenses
- \( y \) = quantity of wheat purchased in quintals

### Step 2: Set Up the Equations
From the problem, we have two scenarios:

1. When the price of wheat is Rs. 250 per quintal, the total expenses are Rs. 1000:
\[ C + 250y = 1000 \quad \text{(Equation 1)} \]

2. When the price of wheat is Rs. 240 per quintal, the total expenses are Rs. 980:
\[ C + 240y = 980 \quad \text{(Equation 2)} \]

### Step 3: Solve the Equations
We will solve these two equations simultaneously to find the values of \( C \) and \( y \).

#### Step 3.1: Subtract Equation 2 from Equation 1
\[ (C + 250y) - (C + 240y) = 1000 - 980 \]
This simplifies to:
\[ 10y = 20 \]
So,
\[ y = 2 \quad \text{(quantity of wheat purchased)} \]

#### Step 3.2: Substitute \( y \) back into one of the equations
We can substitute \( y = 2 \) into Equation 1 to find \( C \):
\[ C + 250(2) = 1000 \]
This simplifies to:
\[ C + 500 = 1000 \]
Thus,
\[ C = 1000 - 500 = 500 \]

### Step 4: Find Total Monthly Expenses when Wheat Price is Rs. 350
Now, we need to find the total monthly expenses when the cost of wheat is Rs. 350 per quintal:
\[ \text{Total Expenses} = C + 350y \]
Substituting the values of \( C \) and \( y \):
\[ \text{Total Expenses} = 500 + 350(2) \]
This simplifies to:
\[ \text{Total Expenses} = 500 + 700 = 1200 \]

### Final Answer
The total monthly expenses of the family when the cost of wheat is Rs. 350 a quintal is **Rs. 1200**.

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