Question

At what time, between 3 o'clock and 4 o'clock, will both the needles coincide with each other?

• A. 17 past 3
• B. 13 past 3
• C. 16 past 3
• D. 16 past 3

Answer 1

The correct option is D

16 past 3

At 3 o'clock, the minute hand is 15 min. apart from the hour hand.

To be coincident, it must gain 15 min.

55 min. are gained in 60 min.

15 min. are gained in $\left(\frac{60}{55}\times 15\right)$min . = 16$\frac{4}{11}$ min.

$\therefore$The hands are coincident at $16\frac{4}{11}$ min. past 3.