Question

At what time between $7$ and $8$ o' clock will the hands of a clock be in the same straight line but, not together?

• A. $5$ min. past $7$
• B. $5\frac{2}{11}$ min. past $7$
• C. $5\frac{3}{11}$ min. past $7$
• D. $5\frac{5}{11}$ min. past $7$

Answer 1

The correct option is D $5\frac{5}{11}$ min. past $7$

When the hands of the clock are in the same straight line but not together, they are $30$ minute spaces apart. At $7$ o'clock, they are $25$ min. spaces apart.
$\therefore$ Minute hand will have to gain only $5$ min. spaces.
$55$ min. spaces are gained in $60$ min.
$5$ min. spaces are gained in $\left(\frac{60}{55}\times 5\right)$ min. $=5\frac{5}{11}$ min.
$\therefore$ Required time $=5\frac{5}{11}$ min. past $7$