The price of sugar is increased by 20% By what percentage must one cut down on the consumption of sugar so that no extra amount has to be incurred on sugar?

Options

A. `16""2/3%`
B. `83""1/3%`
C. `20%`
D. `80%`

Answer

To solve the problem step by step, we can follow this method:

### Step 1: Understand the Initial Price
Let’s assume the initial price of sugar is \( P \) (in rupees).

### Step 2: Calculate the Increased Price
Since the price of sugar is increased by 20%, the new price of sugar becomes:
\[ \text{New Price} = P + 0.20P = 1.20P \]

### Step 3: Determine the Consumption Before Price Increase
Let’s assume the initial quantity of sugar consumed is \( Q \) (in kg or any unit).

### Step 4: Calculate the Initial Total Cost
The initial total cost of sugar before the price increase is:
\[ \text{Initial Total Cost} = P \times Q \]

### Step 5: Calculate the New Total Cost After Price Increase
After the price increase, if the quantity consumed is reduced to \( Q' \), the new total cost becomes:
\[ \text{New Total Cost} = 1.20P \times Q' \]

### Step 6: Set the Costs Equal
To ensure that no extra amount is incurred, we set the initial total cost equal to the new total cost:
\[ P \times Q = 1.20P \times Q' \]

### Step 7: Simplify the Equation
We can cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ Q = 1.20Q' \]

### Step 8: Solve for \( Q' \)
Now, we can express \( Q' \) in terms of \( Q \):
\[ Q' = \frac{Q}{1.20} = \frac{Q}{\frac{6}{5}} = \frac{5Q}{6} \]

### Step 9: Calculate the Reduction in Consumption
The reduction in consumption is:
\[ \text{Reduction} = Q - Q' = Q - \frac{5Q}{6} = \frac{Q}{6} \]

### Step 10: Calculate the Percentage Reduction
To find the percentage reduction in consumption:
\[ \text{Percentage Reduction} = \left( \frac{\text{Reduction}}{Q} \right) \times 100 = \left( \frac{\frac{Q}{6}}{Q} \right) \times 100 = \frac{100}{6} \approx 16.67\% \]

### Final Answer
Thus, one must cut down on the consumption of sugar by approximately **16.67%** to avoid incurring any extra amount.

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