Question : The sum of three numbers is 2, the 1st number is $\frac{1}{2}$ times the 2nd number and the 3rd number is $\frac{1}{4}$ times the 2nd number. The 2nd number is:
Option 1: $\frac{7}{6}$
Option 2: $\frac{8}{7}$
Option 3: $\frac{9}{8}$
Option 4: $\frac{10}{9}$
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Correct Answer: $\frac{8}{7}$
Solution :
Let the second number be $x$, the first number be $ \frac{x}{2}$ and the third number be $\frac{x}{4}$.
According to the question,
⇒ $\frac{x}{2}+x+\frac{x}{4}=2$
⇒ $\frac{2x+4x+x}{4} =2$
⇒ $2x+4x+x=8$
⇒ $7x=8$
$\therefore x=\frac{8}{7}$
Hence, the correct answer is $\frac{8}{7}$.
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