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Four bells toll at intervals 4, 7, 12 & 84 seconds. The bells toll together at 7 o’clock. How many times will they again toll together in 28 minutes?
- a)15
- b)20
- c)25
- d)30
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Four bells toll at intervals 4, 7, 12 & 84 seconds. The bells toll...
They will toll together for a 'common multiple' of (4,7,12,84), which is the l.c.m of these numbers.
4= 2^2
7 = 7
12 = 2^2 * 3
84 = 12 * 7 = 2^2 * 3 * 7
l.c.m(4,7,12,84) = 2^2 * 3 * 7 = 84 s
84 s = 1 min 24 sec
Hence they will toll together 84 seconds after 5 o'clock or 5:01:24 hrs ( 1 min 24 sec past 5 o'clock)
28 mins = 28*60 = 1680 sec
84 sec== toll 1 time
1680 sec== X times
X = 20 times
Hence,
They toll together at 5:01:24 hrs
In 28 mins they toll (together) 20 times.
Most Upvoted Answer
Four bells toll at intervals 4, 7, 12 & 84 seconds. The bells toll...
To find the least common multiple (LCM) of 4, 7, and 12, we can list the multiples of each number and find the smallest number that appears in all three lists:
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, ...
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, ...
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, ...
From the lists, we can see that the smallest number that appears in all three lists is 84. Therefore, the four bells will toll together at every 84 minutes.
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, ...
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, ...
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, ...
From the lists, we can see that the smallest number that appears in all three lists is 84. Therefore, the four bells will toll together at every 84 minutes.
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Four bells toll at intervals 4, 7, 12 & 84 seconds. The bells toll...
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Four bells toll at intervals 4, 7, 12 & 84 seconds. The bells toll together at 7 o’clock. How many times will they again toll together in 28 minutes?a)15b)20c)25d)30Correct answer is option 'B'. Can you explain this answer?
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