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
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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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