Every month the Chopra family consumes 25 kg rice and 9 kg dal. The price of rice is 20% of the price of dal and they spend a total of Rs.3,500 on the rice and dal per month. If the price of dal is increased by 20%, then what should be the percentage reduction in rice consumption for the expenditure to remain the same? Given that the price of rice and consumption of dal is constant.

1. 36%

2. 40%

3. 25%

4. 24%

We are given the following information:

1. The Chopra family consumes 25 kg of rice and 9 kg of dal every month.
2. The price of rice is 20% of the price of dal.
3. They spend a total of Rs. 3,500 per month on rice and dal.
4. The price of dal increases by 20%, and we need to find the percentage reduction in rice consumption so that the total expenditure remains Rs. 3,500.

Let’s define:

- \( p_d \) = price of dal (per kg)
- \( p_r \) = price of rice (per kg)

From the given information:
- \( p_r = 0.2 \cdot p_d \) (since the price of rice is 20% of the price of dal).

### Step 1: Calculate the initial expenditure on rice and dal
The total expenditure on rice and dal initially is Rs. 3,500, which can be written as:

\[
\text{Expenditure on rice} + \text{Expenditure on dal} = 3,500
\]

Substituting the expenditures:

\[
25 \cdot p_r + 9 \cdot p_d = 3,500
\]

Since \( p_r = 0.2 \cdot p_d \), substitute \( p_r \) in the equation:

\[
25 \cdot (0.2 \cdot p_d) + 9 \cdot p_d = 3,500
\]

Simplifying:

\[
5 \cdot p_d + 9 \cdot p_d = 3,500
\]

\[
14 \cdot p_d = 3,500
\]

\[
p_d = 250
\]

Thus, the price of dal \( p_d = 250 \) Rs/kg, and the price of rice \( p_r = 0.2 \cdot 250 = 50 \) Rs/kg.

### Step 2: Calculate the initial expenditure on rice and dal

- Expenditure on rice = \( 25 \cdot 50 = 1,250 \) Rs.
- Expenditure on dal = \( 9 \cdot 250 = 2,250 \) Rs.

So the total expenditure is \( 1,250 + 2,250 = 3,500 \) Rs, which matches the given total.

### Step 3: Calculate the new price of dal after the 20% increase

The new price of dal after the 20% increase:

\[
\text{New price of dal} = p_d + 0.2 \cdot p_d = 250 + 0.2 \cdot 250 = 250 + 50 = 300 \text{ Rs/kg}
\]

### Step 4: New total expenditure on dal

The expenditure on dal remains the same in terms of consumption (9 kg), but the price has increased:

\[
\text{New expenditure on dal} = 9 \cdot 300 = 2,700 \text{ Rs}
\]

### Step 5: Calculate the new expenditure on rice

To maintain the total expenditure at Rs. 3,500, the total expenditure on rice must be:

\[
3,500 - 2,700 = 800 \text{ Rs}
\]

Let the new consumption of rice be \( x \) kg. Since the price of rice remains the same at Rs. 50 per kg:

\[
x \cdot 50 = 800
\]

\[
x = \frac{800}{50} = 16 \text{ kg}
\]

### Step 6: Calculate the percentage reduction in rice consumption

The initial consumption of rice was 25 kg, and the new consumption is 16 kg. The percentage reduction in rice consumption is:

\[
\text{Percentage reduction} = \frac{25 - 16}{25} \times 100 = \frac{9}{25} \times 100 = 36\%
\]

Thus, the percentage reduction in rice consumption is **36%**.

### Final Answer:
The correct option is **1. 36%**.

Would you like more details or have any questions? Here are some related questions:

1. How is the percentage increase calculated in such price-related problems?
2. What other methods can be used to solve problems involving proportional consumption and expenditure?
3. Can the same method be used for other commodities like vegetables or fruits?
4. How does inflation affect such percentage reduction calculations?
5. How would the problem change if the price of rice also increased?

**Tip:** When working with percentage changes, always express one variable in terms of another to simplify the problem.

Every month the Chopra family consumes 25 kg rice and 9 kg dal. The price of rice is 20% of the price of dal and they spend a total of Rs.3,500 on the rice and dal per month. If the price of dal is increased by 20%, then what should be the percentage reduction in rice consumption for the expenditure to remain the same? Given that the price of rice and consumption of dal is constant.

Solve a real-life algebra problem where the Chopra family must reduce their rice consumption after a 20% increase in the price of dal. Learn how to calculate the percentage reduction to maintain the same expenditure, with a detailed step-by-step solution.

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