Question : Due to a price hike of 20%, 4 kg less sugar is available for Rs. 120. What is the initial price per kg of sugar?
Option 1: Rs. 5 per kg
Option 2: Rs. 4 per kg
Option 3: Rs. 6 per kg
Option 4: Rs. 5.5 per kg
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Correct Answer: Rs. 5 per kg
Solution : Let the initial price of the sugar be Rs. $x$ per kg. Increase in price is 20%, it means increased price $=\frac{120x}{100}=\frac{6x}{5}$ According to the question, Initial quantity – Current quantity = Reduction in quantity ⇒ $\frac{120}{x} -\frac{120}{ \frac{6x}{5}} = 4$ ⇒ $\frac{120}{x} -\frac{600}{ {6x}} = 4$ ⇒ $\frac{120}{x} -\frac{100}{ {x}} = 4$ ⇒ $\frac{20}{x} = 4$ $\therefore x = 5$ Hence, the correct answer is Rs. 5 per kg.
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