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Four clocks were set right at the same time. One clock gains 'a' minutes in a day, second clock loses 'b' minutes in a day, third clock gains 'c' minutes in a day and the fourth clock gains 'd' minutes. After how much time will all the clocks again show the correct time simultaneously if a + b + c + d = 1 hour, a : b = c : d = 2 : 1 and b : d = 3 : 1?
  • a)
    3 hours
  • b)
    12 hours
  • c)
    24 hours
  • d)
    144 days
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Four clocks were set right at the same time. One clock gains 'a' minu...
To solve this problem, let's consider the time it takes for each clock to gain or lose a certain number of minutes.

Let:
- a = the number of minutes gained by the first clock in a day
- b = the number of minutes lost by the second clock in a day
- c = the number of minutes gained by the third clock in a day
- d = the number of minutes gained by the fourth clock in a day

Since a:b = c:d = 2:1, we can write:
c = (1/2)a
d = (1/2)b

Let's assume that after x days, all the clocks show the correct time simultaneously.

Clock 1 gains a minutes in a day, so in x days, it will gain ax minutes.
Clock 2 loses b minutes in a day, so in x days, it will lose bx minutes.
Clock 3 gains c minutes in a day, so in x days, it will gain cx minutes.
Clock 4 gains d minutes in a day, so in x days, it will gain dx minutes.

Now, let's analyze the time it takes for each clock to show the correct time again.

Clock 1 and Clock 3:
Both clocks gain minutes, so the time it takes for them to show the correct time again will be a multiple of the least common multiple (LCM) of a and c.

LCM(a, c) = LCM(a, (1/2)a) = a

Clock 2 and Clock 4:
Both clocks lose or gain minutes, so the time it takes for them to show the correct time again will be a multiple of the LCM of b and d.

LCM(b, d) = LCM(b, (1/2)b) = b

To find the time it takes for all the clocks to show the correct time simultaneously, we need to find the LCM(a, b).

Given that a:b = 2:1 and b:d = 3:1, we can write:
b = (1/3)d
a = 2b = (2/3)d

Substituting these values into LCM(a, b):

LCM(a, b) = LCM((2/3)d, (1/3)d) = d

Therefore, it will take d days for all the clocks to show the correct time simultaneously.

Since it is given that a:b = c:d = 1 hour, and we know that there are 24 hours in a day, d = 24.

Hence, all the clocks will show the correct time simultaneously after 24 days, which is equivalent to 24*60 = 1440 minutes.

Therefore, the correct answer is option D) 144 days.
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Community Answer
Four clocks were set right at the same time. One clock gains 'a' minu...
Let d be k,
then b = 3k, c = 2k and a = 6k
a + b + c + d = 1 hour = 60 minutes.
So,
6k + 3k + 2k + k = 60 minutes
K = 5 minutes
So, the first clock gains 30 minutes in 1 day,
so it will show the correct time when it gains 24 hours and it will be done in
The second clock loses 15 minutes in a day, so it will show correct time after losing 24 hours and so
The third clock gains 10 minutes in a day, so it will show correct time after gaining 24 hours =
The fourth clock gains 5 minutes per day, so it will show correct time after gaining 24 hours in
All 4 clocks will show correct time simultaneously after N days where N is LCM of 48, 96, 144 and 480 N = 1440 days.
So, all the clocks will show correct time simultaneously after 1440 days.
Hence, the correct option is (d).
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Four clocks were set right at the same time. One clock gains 'a' minutes in a day, second clock loses 'b' minutes in a day, third clock gains 'c' minutes in a day and the fourth clock gains 'd' minutes. After how much time will all the clocks again show the correct time simultaneously if a + b + c + d = 1 hour, a : b = c : d = 2 : 1 and b : d = 3 : 1?a)3 hoursb)12 hoursc)24 hoursd)144 daysCorrect answer is option 'D'. Can you explain this answer?
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