Question

At what time (approx) between 8 and 9 o'clock will the hands of a clock be in the same straight line but not together?

• A. 8 : 03
• B. 8 : 37
• C. 8 : 11
• D. 8 : 46

Answer 1

The correct option is C

8 : 11

If we assume a clock in ${360}^{\circ }$. There are 12 hours represented in a clock. Between each hour we cover $\frac{360}{12}={30}^{\circ }$. Between 8 to 9 o'clock , the angle will be ${240}^{\circ }$ to ${270}^{\circ }$.

For hour and minute hand to be in the same line but not together they must be at 180 degree apart from each other.
Checking the difference for all the provided options, we get

For minute hand , at 11th minute it will be at $\frac{360}{60}\times 11=66$.

But for 11th minute the hour hand will be at $240+\frac{360}{60}\times 11$ (30 degrees between two hours divided into 60 minutes)

$=240+5.5=245.5$
$245.5-66=179.5$ ( ${180}^{\circ }$ approx )

Or

Between 8 to 9 o’clock , the angle will be ${240}^{\circ }$ to ${270}^{\circ }$. If we subtract 180 degree from both we will get ${60}^{\circ }$ to ${90}^{\circ }$. Converting these into minutes
${60}^{\circ }$ = 10 minutes
${90}^{\circ }$ = 15 minutes
Our answer will be between 8:10 to 8:15
Hence, 8:11 is the correct answer.