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 $25min.$ spaces apart.
$\therefore$ Minute hand will have to gain only $5$ min. spaces.
$55min.$ spaces are gained in $60min.$
$5min.$ spaces are gained in $(\frac{60}{55}\times 5)min.=5\frac{5}{11}min.$
$\therefore$ Required time $=5\frac{5}{11}$ min. past $7$.