A mechanical grandfather clock is at present showing 7 hr 40 min 6 sec. Assuming that it loses 4 seconds in every hour, what time will it show after exactly $6 \frac{1}{2}$ hours?
(a)14 hr 9 min 34 sec
(b)14 hr 9 min 40 sec
(c)14 hr 10 min 6 sec
(d)14 hr 10 min 32 sec
Answer
Answer (as printed): B
Explanation
Time lost in $6 \frac{1}{2}$ hours $=\left(6 \frac{1}{2} \times 4\right) \mathrm{sec}=26 \mathrm{sec}$. Correct time after $6 \frac{1}{2}$ hours $=7 \mathrm{hr} 40 \mathrm{min} 6 \mathrm{sec}+6 \mathrm{hr}$ $30 \min =14 \mathrm{hr} 10 \mathrm{min} 6 \mathrm{sec}$. Time shown by the clock $=14 \mathrm{hr} 10 \mathrm{min} 6 \mathrm{sec}-26 \mathrm{sec}$ = 14 hr 9 min 40 sec.