If the price of sugar increases by 20%, one can buy 2 kg less for Rs. 50. What is the amount of sugar that could be bought be fore price hike?

Options

A. 10kg.
B. 12kg.
C. 14kg.
D. 16kg.

Answer

To solve the problem, we need to determine the amount of sugar that could be bought before the price hike. Let's break down the solution step-by-step:

1. **Define Variables:**
- Let the original price of sugar per kg be \( P \) (in Rs).
- Let the original quantity of sugar that could be bought for Rs. 50 be \( Q \) (in kg).

2. **Price Increase:**
- The price of sugar increases by 20%. Therefore, the new price per kg is \( P + 0.2P = 1.2P \).

3. **New Quantity:**
- After the price increase, the quantity of sugar that can be bought for Rs. 50 is \( Q - 2 \) kg.

4. **Formulate Equations:**
- Before the price hike: \( Q = \frac{50}{P} \)
- After the price hike: \( Q - 2 = \frac{50}{1.2P} \)

5. **Set Up the Equation:**
- Substitute \( Q \) from the first equation into the second equation:
\[ \frac{50}{P} - 2 = \frac{50}{1.2P} \]

6. **Solve for \( P \):**
- Multiply both sides by \( 1.2P \) to clear the denominators:
\[ 1.2P \left( \frac{50}{P} - 2 \right) = 50 \]
- Simplify:
\[ 60 - 2.4P = 50 \]
- Rearrange to solve for \( P \):
\[ 60 - 50 = 2.4P \]
\[ 10 = 2.4P \]
\[ P = \frac{10}{2.4} = \frac{100}{24} = \frac{25}{6} \approx 4.17 \text{ Rs/kg} \]

7. **Find the Original Quantity \( Q \):**
- Use \( P \) to find \( Q \):
\[ Q = \frac{50}{P} = \frac{50}{\frac{25}{6}} = 50 \times \frac{6}{25} = 12 \text{ kg} \]

Thus, the amount of sugar that could be bought before the price hike is **12 kg**.