question_answer

4 bells ring at intervals of 30 min, 1 h, \[1\frac{1}{2}\]h and 1 h 45 min, respectively. All the bells ring simultaneously at 12 noon. They will again ring simultaneously at

A)  12 mid night                 

B)  3 am

C)  6 am               

D)  9 am

Correct Answer: D

Solution :

\[1\frac{1}{2}\]h = 90 min 1 h and 45 min = 105 min 1 h = 60 min \[\therefore \]LCM of 30 min, 60 min, 90 min and 105 min \[\therefore \]LCM\[=3\times 5\times 2\times 2\times 3\times 7=1260\]min 1260 min\[=\frac{1260}{60}=21\,\,\text{h}\] \[\therefore \]The bell will again ring simultaneously after 21 h. \[\therefore \]Time will be = 12 noon + 21 hours = 9 am