Question

After $\text{9 o ' clock}$ at what time between $\text{9 p.m. and 10 p.m.}$ will the hour and minute hands of a clock point in opposite direction ?

• A. $\text{15 minutes past 9}$
• B. $\text{16 minutes past 9}$
• C. $16\frac{4}{11}\text{minutes past 9}$
• D. $17\frac{1}{11}\text{minutes past 9}$

Answer 1

Answer: (C)

$16\frac{4}{11}\text{minutes past 9}$

At $\text{9 o ' clock}$, the minute hand is $9\times 5=45\text{minute}-\text{spaces behind the hour hand}$.
Therefore, the minute hand will have to gain $45-30=10\text{minute space over the hour hand}$.
$\because$ Gain of $\text{55 minute spaces equals 60 minutes}$
$\therefore$ Gain of $\text{15 minute spaces equals}=\frac{60}{55}\times 15=\frac{180}{11}=16\frac{4}{11}$
Therefore, hour and minute hands of a clock point in opposite direction after $\text{9 o ' clock}$ at $16\frac{4}{11}\text{minutes past 9}$.