Question : If the sum of two quantities is equal to three times their difference, then the ratio of the two quantities is:
Option 1: 1 : 3
Option 2: 3 : 1
Option 3: 2 : 1
Option 4: 2 : 3
Correct Answer: 2 : 1
Solution :
Let the numbers be $x$ and $y$.
The sum of the number is $x + y$.
Three times the difference be $3(x-y)$.
According to the given conditions,
$x + y = 3 (x - y)$
$⇒ x + y = 3x - 3y$
$⇒ 2x = 4y$
$⇒ x = 2y$
⇒ $\frac{x}{y}=\frac{2}{1}$
Thus, $x:y = 2:1$
Hence, the correct answer is 2 : 1.
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