Question : Three numbers are in the ratio $\frac{4}{5}: \frac{5}{6}: \frac{9}{10}$. The difference between the smallest and the greatest numbers is 12. Find the number which is neither the smallest nor the greatest.
Option 1: 96
Option 2: 108
Option 3: 100
Option 4: 104

Question

Question : Three numbers are in the ratio $\frac{4}{5}: \frac{5}{6}: \frac{9}{10}$. The difference between the smallest and the greatest numbers is 12. Find the number which is neither the smallest nor the greatest.

Option 1: 96

Option 2: 108

Option 3: 100

Option 4: 104

Team Careers360 · Accepted Answer

Correct Answer: 100

Solution : Three numbers are in the ratio $\frac{4}{5}: \frac{5}{6}: \frac{9}{10}$.
LCM of 5, 6, and 10 is 30.
So, $\frac{4}{5}: \frac{5}{6}: \frac{9}{10}$ = $\frac{4}{5} imes 30: \frac{5}{6} imes 30: \frac{9}{10} imes 30=24:25:27$
The numbers can be simplified and written as $24x,25x,$ and $27x$.
According to the question,
$27x -24x = 12$
$⇒3x = 12$
$ herefore x = 4$
The number which is neither the smallest nor the greatest $=25x = 25 imes 4 = 100$
Hence, the correct answer is 100.

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Question : Three numbers are in the ratio 45:56:910. The difference between the smallest and the greatest numbers is 12. Find the number which is neither the smallest nor the greatest.Option 1: 96Option 2: 108Option 3: 100Option 4: 104

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Question : Three numbers are in the ratio $\frac{4}{5} : \frac{5}{6} : \frac{9}{10}$ . The difference between the smallest and the greatest numbers is 12. Find the number which is neither the smallest nor the greatest.
Option 1: 96
Option 2: 108
Option 3: 100
Option 4: 104