It is between 3 P.M. and 4 P.M. and the distance between the hour and the minute hand of clock is 18 minute spaces. What time does the clock show?
(a)3.12 P.M.
(b)3.27 P.M.
(c)3.31 P.M.
(d)3.36 P.M.
Answer
Answer (as printed): D
Explanation
At 3 o' clock, the minute hand is 15 min spaces behind the hour hand. Thus, the minute hand has to gain $(15+18)=33$ minute spaces. 55 min are gained in 60 min. 33 min are gained in $\left(\frac{60}{55} \times 33\right)=24 \min$. ∴ The hands will be 18 min spaces apart at 3:36 P.M.
Explanation as extracted from the printed page; notation may be imperfect.