Question : 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 before the price hike?
Option 1: 10 kg
Option 2: 12 kg
Option 3: 14 kg
Option 4: 16 kg
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Correct Answer: 12 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
⇒ $\frac{50}{x} -\frac{50}{ \frac{6x}{5}} = 2$
⇒ $\frac{50}{x} - \frac{250}{ {6x}}= 2$
⇒ $\frac{300-250}{ {6x}}= 2$
$\therefore x = \frac{50}{12}$
Initial quantity $= \frac{50}{(\frac{50}{12})} = 12$ kg
Hence, the correct answer is 12 kg.
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