At what time, in minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each other?
(a)$5 \frac{1}{11}^{\prime \prime}$ past
(b)$12 \frac{4}{11}^{\prime \prime}$ past
(c)$13 \frac{4}{11}^{\prime \prime}$ past
(d)$16 \frac{4}{11}^{\prime \prime}$ past (R.R.B., 2002)
Answer
Answer (as printed): D
Explanation
At 3 o'clock, the minute hand is 15 min. spaces apart from the hour hand. To be coincident, it must gain 15 min. spaces. 55 min . are gained in 60 min . 15 min. are gained in $\left(\frac{60}{55} \times 15\right) \min .=16 \frac{4}{11} \min$. ∴ The hands are coincident at $16 \frac{4}{11} \mathrm{min}$. past 3.