If the price of sugar increases by 10%, by what percentage a housewife should reduce the consumption of sugar so that expense is not increased?

Options

A. 10%
B. 9.1%
C. 7.1%
D. 20%

Answer

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

### Step 1: Determine the initial price of sugar
Let the initial price of sugar be Rs. 100 per kg.

### Step 2: Calculate the new price after a 10% increase
The price of sugar increases by 10%. Therefore, the new price can be calculated as follows:
\[ \text{New Price} = \text{Old Price} + \left(\frac{10}{100} \times \text{Old Price}\right) \]
Substituting the old price:
\[ \text{New Price} = 100 + \left(\frac{10}{100} \times 100\right) = 100 + 10 = 110 \text{ Rs. per kg} \]

### Step 3: Determine the amount of money that can be spent on sugar to keep expenses the same
The housewife wants to keep her expenses the same as before. Therefore, she will still spend Rs. 100 on sugar.

### Step 4: Calculate the quantity of sugar that can be bought at the new price
To find out how much sugar she can buy at the new price of Rs. 110 per kg, we use the formula:
\[ \text{Quantity of sugar} = \frac{\text{Total Expense}}{\text{New Price}} = \frac{100}{110} \text{ kg} \]

### Step 5: Calculate the initial quantity of sugar that could be bought
At the old price of Rs. 100 per kg, the quantity of sugar that could be bought was:
\[ \text{Initial Quantity} = \frac{100}{100} = 1 \text{ kg} \]

### Step 6: Calculate the reduction in quantity of sugar
Now, we find the reduction in quantity:
\[ \text{Reduction in Quantity} = \text{Initial Quantity} - \text{New Quantity} = 1 - \frac{100}{110} \]
Calculating the new quantity:
\[ \text{New Quantity} = \frac{100}{110} = \frac{10}{11} \text{ kg} \]
Thus,
\[ \text{Reduction in Quantity} = 1 - \frac{10}{11} = \frac{1}{11} \text{ kg} \]

### Step 7: Calculate the percentage reduction in consumption
To find the percentage reduction in consumption, we use the formula:
\[ \text{Percentage Reduction} = \left(\frac{\text{Reduction in Quantity}}{\text{Initial Quantity}}\right) \times 100 \]
Substituting the values:
\[ \text{Percentage Reduction} = \left(\frac{\frac{1}{11}}{1}\right) \times 100 = \frac{100}{11} \approx 9.09\% \]

### Step 8: Round off the answer
Rounding off the percentage reduction gives us approximately 9.1%.

### Final Answer
The housewife should reduce her consumption of sugar by approximately **9.1%** to keep her expenses the same.

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