Question : The sum of three fractions is $2\frac{11}{24}$. On dividing the largest faction by the smallest fraction, $\frac{7}{6}$ is obtained which is $\frac{1}{3}$ greater than the middle fraction. The smallest fraction is:
Option 1: $\frac{5}{8}$
Option 2: $\frac{3}{4}$
Option 3: $\frac{5}{6}$
Option 4: $\frac{3}{7}$
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Correct Answer: $\frac{3}{4}$
Solution :
Let the largest fraction be $x$, the middle fraction be $y$ and the smallest fraction be $z$.
From the question, on dividing the largest fraction by the smallest fraction i.e. $\frac{x}{z}=\frac{7}{6}⇒x=\frac{7}{6}z$
Now, the middle fraction is $\frac{1}{3}$ more than $\frac{7}{6}$.
$ y=\frac{7}{6}-\frac{1}{3 }=\frac{5}{6}$
Putting the values according to the question, we get,
$x+y+z=2\frac{11}{24}$
⇒ $\frac{7}{6}z +\frac{5}{6}+z =2\frac{11}{24}$
⇒ $\frac{7z+5+6z}{6}=\frac{59}{24}$
⇒ $\frac{13z+5}{6}=\frac{59}{24}$
⇒ $\frac{13z}{1}=\frac{59}{4}-5$
⇒ $13z=\frac{39}{4}$
$\therefore z =\frac{3}{4}$
Hence, the correct answer is $\frac{3}{4}$.
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