Question : If $(7 x+y):(7 x–y)=7: 2$, then what is the value of $x: y$?
Option 1: 9 : 35
Option 2: 11 : 42
Option 3: 6 : 41
Option 4: 17 : 52
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Correct Answer: 9 : 35
Solution : Given: $(7 x+y):(7 x–y)=7: 2$ Cross-multiply to find the value of $x:y$ ⇒ $\frac{(7 x+y)}{(7 x–y)}=\frac{7}{2}$ ⇒ $14 x+2y=49 x–7y$ ⇒ $49 x–14x=2y+7y$ ⇒ $35x=9y$ ⇒ $\frac{x}{y}=\frac{9}{35}$ ⇒ $x:y=9:35$ Hence, the correct answer is 9 : 35.
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