1.

4 bells ring at intervals of 30 minutes, 1 hour, \(1\frac{1}{2}\) hour and 1 hour 45 minutes respectively. All the bells ring simultaneously at 12 noon. They will again ring simultaneously at:1). 12 mid night2). 3 a.m.3). 6 a.m.4). 9 a.m.

Answer»

Given data-

4 bells ring at INTERVALS of 30 MINUTES, 1 hour, $(1\frac{1}{2})$ hour and 1 hour 45 minutes respectively

Converting them into fractions

30min = 1/2 hour

1 hour = 1/1 hour

$(1\frac{1}{2})$ Hour = 3/2 hour

1 hour 45 minutes = 7/4 hour

To find NEXT simultaneous ring of 4 bells

Let’s find L.C.M. of these fractions:

L.C.M of fractions = (L.C.M of numerators)/(H.C.F of denominators)

⇒ LCM of fractions $(= {\rm{\;}}\frac{{{\rm{L}}.{\rm{C}}.{\rm{M\;of\;}}\left( {1,1,3,7} \right)}}{{{\rm{H}}.{\rm{C}}.{\rm{F\;of}}\left( {2,1,2,4} \right)}})$

⇒ LCM of fractions = 21/1 = 21

∴ Bells will ring simultaneously after 21 HOURS.

Counting 21 hours after 12 noon.

They will ring on 9 am. On next day.


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