Question

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

• A. ${5\frac{1}{4}}^{\prime \prime }$
• B. ${12\frac{4}{11}}^{\prime \prime }$
• C. ${13\frac{4}{11}}^{\prime \prime }$
• D. ${16\frac{4}{11}}^{\prime \prime }$

Answer 1

Answer: (D)

${16\frac{4}{11}}^{\prime \prime }$

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 $(\frac{60}{55}\times 15)min.=16\frac{4}{11}$min.
$\therefore$ The hands are coincident at $16\frac{4}{11}$ min. past $3$.