The price of sugar is increased by 21%. A person wants to increase his expenditure by 12% only. By what percent should he decrease his consumption , nearest to one decimal place?
चीनी की कीमत 21% से बढ़ जाती है| एक व्यक्ति अपना व्यय केवल 12% बढ़ाना चाहता है | उसे अपनी खपत में कितने प्रतिशत ( एक दशमलव स्थान तक सही ) की कमी करनी चाहिए ?

Options

A. 0.074
B. 0.072
C. 0.076
D. 0.4

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Understand the initial conditions
Let’s assume the initial price of sugar is Rs. 100. Therefore, the initial expenditure can be calculated based on the initial consumption.

### Step 2: Calculate the new price after the increase
The price of sugar is increased by 21%.
- New Price = Initial Price + (21% of Initial Price)
- New Price = 100 + (21/100 * 100) = 100 + 21 = Rs. 121

### Step 3: Determine the desired expenditure
The person wants to increase his expenditure by 12%.
- Initial Expenditure = Initial Price * Initial Consumption (let's assume consumption is 1 unit for simplicity)
- Initial Expenditure = 100 * 1 = Rs. 100
- New Expenditure = Initial Expenditure + (12% of Initial Expenditure)
- New Expenditure = 100 + (12/100 * 100) = 100 + 12 = Rs. 112

### Step 4: Set up the equation for new consumption
Let the new consumption be \( C \). The new expenditure can also be expressed as:
- New Expenditure = New Price * New Consumption
- 112 = 121 * C

### Step 5: Solve for new consumption
Now we can solve for \( C \):
- C = 112 / 121
- C ≈ 0.9256 (approximately)

### Step 6: Calculate the decrease in consumption
The initial consumption was 1 unit. The new consumption is approximately 0.9256 units.
- Decrease in consumption = Initial Consumption - New Consumption
- Decrease in consumption = 1 - 0.9256 = 0.0744 units

### Step 7: Calculate the percentage decrease in consumption
To find the percentage decrease:
- Percentage Decrease = (Decrease in Consumption / Initial Consumption) * 100
- Percentage Decrease = (0.0744 / 1) * 100 ≈ 7.44%

### Step 8: Round to one decimal place
Rounding 7.44% to one decimal place gives us approximately 7.4%.

### Final Answer
The person should decrease his consumption by approximately **7.4%**.

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