Question : The sum of the two numbers is 520. If the bigger number is decreased by 4% and the smaller number is increased by 12%, then the numbers obtained are equal. The smaller number is:
Option 1: 280
Option 2: 210
Option 3: 240
Option 4: 300
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Correct Answer: 240
Solution :
Given: The sum of two numbers is 520.
Let the bigger number be $a$ and the smaller number be $(520 - a)$.
The bigger number is decreased by 4% and the smaller number is increased by 12%.
So, $a×\frac{96}{100}=(520 - a)×\frac{112}{100}$
⇒ $96a=(520 - a)×112$
⇒ $208a=520×112$
⇒ $a=\frac{520×112}{208}=280$
Smaller number = (520 – 280) = 240
Hence, the correct answer is 240.
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