When the price of rice is increased by 25 percentage , a family reduces its consumption such that the expenditure is only 10 percentage more than before . If 40 kg of rice is consumed by family before , then find the new consumption of family .

Options

A. `35.2`
B. `35.2`
C. `36.2`
D. `37.2`

Explanation

To solve the problem step by step, let's break it down:

### Step 1: Understand the Initial Conditions
The family initially consumes 40 kg of rice. Let’s denote the original price of rice as \( P \).

### Step 2: Calculate the New Price of Rice
The price of rice is increased by 25%. Therefore, the new price \( P' \) can be calculated as:
\[ P' = P + 0.25P = 1.25P \]

### Step 3: Calculate the Original Expenditure
The original expenditure \( E \) of the family can be calculated as:
\[ E = \text{Price} \times \text{Consumption} = P \times 40 \]

### Step 4: Calculate the New Expenditure
The problem states that the new expenditure is 10% more than the original expenditure. Thus, the new expenditure \( E' \) is:
\[ E' = E + 0.10E = 1.10E \]
Substituting \( E \):
\[ E' = 1.10(P \times 40) = 44P \]

### Step 5: Set Up the Equation for New Consumption
Let the new consumption be \( x \) kg. The new expenditure can also be expressed as:
\[ E' = P' \times x = 1.25P \times x \]

### Step 6: Equate the Two Expressions for New Expenditure
Now, we can set the two expressions for \( E' \) equal to each other:
\[ 1.25P \times x = 44P \]

### Step 7: Solve for New Consumption \( x \)
We can divide both sides by \( P \) (assuming \( P \neq 0 \)):
\[ 1.25x = 44 \]
Now, solve for \( x \):
\[ x = \frac{44}{1.25} = 35.2 \text{ kg} \]

### Conclusion
The new consumption of the family is **35.2 kg**.

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