Question : A number, when subtracted from 3 times the second number, gives a result equal to $\frac{3}{4}$ of the first number. What is the ratio of the first number to the second number?
Option 1: 11 : 6
Option 2: 12 : 7
Option 3: 9 : 5
Option 4: 10 : 7
Correct Answer: 12 : 7
Solution :
Let the two numbers be x and y.
Then, according to the question
3$y$ – $x$ = $\frac{3}{4}$ $x$
We need to find the ratio of the first number to the second number i.e. $x$ : $y$
Simplifying the equation:
3$y$ – $x$ = $\frac{3}{4}$ $x$
⇒ 12$y$ - 4$x$ = 3$x$
⇒ 12$y$ = 7$x$
⇒ $y$ = $\frac{7\text{x}}{12}$
So, $\frac{\text{x}}{\text{y}} = \frac{12}{7}$
Therefore, the required ratio is 12 : 7.
Hence, the correct answer is 12 : 7.
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