Question : A reduction of 10% in the price of a commodity enables a person to buy 25 kg more for Rs. 225. The original price of the commodity per kg was:
Option 1: Rs. 2
Option 2: Re. 1
Option 3: Rs. 2.50
Option 4: Rs.1.50
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Correct Answer: Re. 1
Solution :
Let the original price of the commodity be Rs. $x$ per kg.
Reduction = 10%
New price is 90% of $x$ = $\frac{90}{100}x$ = Rs. $\frac{9}{10}x$
According to the question:
$\frac{225}{\frac{9}{10}x}$–$\frac{225}{x}$ = 25
⇒ $\frac{2250}{9x}$–$\frac{225}{x}$ = 25
⇒ $\frac{2250-2025}{9x}$ = 25
⇒ $\frac{225}{25}$ = $9x$
⇒ $x$ = Re. 1
Hence, the correct answer is Re. 1.
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