Question

A reduction of 20% in the price of sugar enables a person to purchase 6 kg more for Rs. 240. What is the original price per kg of sugar?

• A. Rs.10/kg
• B. Rs. 8/kg
• C. Rs. 6/kg
• D. Rs. 5/kg

Answer 1

The Correct Option is A

To determine the original price per kg of sugar, we start by considering the information given:

A person spends Rs. 240 and with a 20% reduction in price, they can buy 6 kg more sugar.

1. Let the original price per kg be Rs. x.
2. The reduced price after a 20% decrease is \(0.8 \times x = 0.8x\).
3. Let the original quantity bought with Rs. 240 be \(q\) kg. So, \(q = \frac{240}{x}\).
4. At the reduced price, the person can buy 6 kg more, meaning \(\frac{240}{0.8x} = q + 6\).
5. Substituting the value of \(q\):

\(\frac{240}{0.8x} = \frac{240}{x} + 6\)

1. Simplify the equation: \(\frac{240}{0.8x} - \frac{240}{x} = 6\).
2. Find a common denominator:

\(\frac{240x - 240 \times 0.8x}{0.8x \times x} = 6\)

1. Simplify: \(\frac{240x - 192x}{0.8x^2} = 6\)
2. This becomes \(\frac{48x}{0.8x^2} = 6\).
3. Cancel \(x\) from numerator and denominator:

\(\frac{48}{0.8x} = 6\)

1. Rearrange: \(48 = 4.8x\).
2. Solve for \(x\): \(x = \frac{48}{4.8} = 10\).

The original price per kg of sugar is Rs. 10.