Question : The sum of the two numbers is 400. If the bigger number is decreased by 16% and the smaller number is increased by 16%, then the numbers obtained are equal. Find the smaller number.
Option 1: 168
Option 2: 152
Option 3: 144
Option 4: 170
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Correct Answer: 168
Solution :
Given: The sum of the two numbers is 400.
Let the bigger number and the smaller number be $x$ and $y$ respectively.
⇒ $x+y=400$ (equation 1)
According to the question,
$x-\frac{16}{100}x=y+\frac{16}{100}y$
⇒ $\frac{84}{100}x=\frac{116}{100}y$
⇒ $84x=116y$
$\therefore x=\frac{116}{84}y$
Substitute the value in the equation 1,
⇒ $\frac{116}{84}y+y=400$
⇒ $\frac{200y}{84}=400$
⇒ $y=168$
Hence, the correct answer is 168.
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