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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:
- A12 mid night
- B3 a.m.
- C6 a.m.
- D9 a.m.
Answer not set
Discussion 1
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CCommunity
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.
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.