Question

At what time between $9$ and $10$ will the hands of a clock be in the straight line, but not together ?

• A. $16$ minutes past $9$
• B. $16\frac{4}{11}$ minutes past $9$
• C. $16\frac{6}{11}$ minutes past $9$
• D. $16\frac{9}{11}$ minutes past $9$

Answer 1

Answer: (B)

$16\frac{4}{11}$ minutes past $9$

At $9o^{\prime }clock$, the angle between the minute hand and the hour hand is ${90}^0$.
The hour hand moves half degree in one minute and the minute hand moves $6^0$ in one minute.
For them to make ${180}^0$, it has to move $m$ minutes, then
$180=90+(6m-\frac{m}{2})$
$90=\frac{11m}{2}\Rightarrow m=\frac{180}{11}$
$m=16\frac{4}{11}$
It should be $16\frac{4}{11}$ past $9$ for the two hands to be in straight line.
Hence, option B.