When the price of sugar gets raised by 50%, a person increases his expenditure on sugar only by 25%. By what percentage (correct up to two decimal places) should he reduce his consumption of sugar?

Options

A. 1.275
B. 1.575
C. 1.667
D. 1.154

Answer

To solve the problem step by step, we will analyze the situation involving the price increase, expenditure increase, and the consequent reduction in consumption of sugar.

### Step 1: Define Initial Conditions
Let the initial price of sugar be \( P = 100 \) rupees per kg, and let the initial quantity of sugar purchased be \( Q = 10 \) kg.

**Hint:** Choose a simple initial price and quantity to make calculations easier.

### Step 2: Calculate Initial Expenditure
The initial expenditure \( E \) can be calculated as:
\[ E = P \times Q = 100 \times 10 = 1000 \text{ rupees} \]

**Hint:** Remember that expenditure is the product of price and quantity.

### Step 3: Calculate New Price After Increase
The price of sugar is raised by 50%. Therefore, the new price \( P' \) is:
\[ P' = P + (0.50 \times P) = 100 + (0.50 \times 100) = 100 + 50 = 150 \text{ rupees per kg} \]

**Hint:** To find the new price after a percentage increase, multiply the original price by the percentage increase and add it to the original price.

### Step 4: Calculate New Expenditure After Increase
The person increases his expenditure by 25%. Therefore, the new expenditure \( E' \) is:
\[ E' = E + (0.25 \times E) = 1000 + (0.25 \times 1000) = 1000 + 250 = 1250 \text{ rupees} \]

**Hint:** Similar to the price, calculate the new expenditure by adding the increase to the original expenditure.

### Step 5: Calculate New Quantity of Sugar Purchased
Now, we need to find the new quantity \( Q' \) of sugar that can be bought with the new expenditure at the new price:
\[ Q' = \frac{E'}{P'} = \frac{1250}{150} \approx 8.33 \text{ kg} \]

**Hint:** To find the quantity, divide the total expenditure by the price per kg.

### Step 6: Calculate Reduction in Quantity
Now, we calculate the reduction in quantity:
\[ \text{Reduction} = Q - Q' = 10 - 8.33 \approx 1.67 \text{ kg} \]

**Hint:** The reduction is simply the difference between the initial and new quantities.

### Step 7: Calculate Percentage Reduction in Consumption
To find the percentage reduction in consumption, we use the formula:
\[ \text{Percentage Reduction} = \left( \frac{\text{Reduction}}{Q} \right) \times 100 = \left( \frac{1.67}{10} \right) \times 100 \approx 16.67\% \]

**Hint:** To find the percentage, divide the reduction by the original quantity and multiply by 100.

### Final Answer
The percentage by which the person should reduce his consumption of sugar is approximately **16.67%**.

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