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Mr. Alaram designed a new clock, which has 12 divisions as usual, represented by the numbers 1 to 12. But the speed of the minute hand is directly proportional to the digit, which it is going to approach, i.e. if the minute hand is between 1 and 2, its speed is proportional to 2 and if it is between 11 and 12, its speed is proportional to 12. The speed of the minute hand, when it is between 12 and 1 is equal to that of an ordinary clock and both the clocks were set at 9 : 00 am.
What will be the time in the ordinary clock, if the new clock shows 9 : 30 am?
  • a)
    9 : 12 : 15 am
  • b)
    9 : 20 : 15 am
  • c)
    9 : 24 : 15 am
  • d)
    9 : 30 : 15 am
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Mr. Alaram designed a new clock, which has 12 divisions as usual, repr...
Since, in between 12 and 1, the speed of minutes hand is similar to that of an ordinary clock, it take 5 minutes to cover first division.
Then its speed will become twice, because, the hand is between 1 and 2.
So, it takes  minutes. Between 2 and 3, the speed becomes thrice and takes  minutes.
So, in total it takes  minutes to reach 6 (9 : 30 am).
= 5 =  minutes = 12¼ minutes.
So, ordinary clock shows 9 hours 12 minutes 15 seconds.
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Mr. Alaram designed a new clock, which has 12 divisions as usual, repr...
First, let's understand the concept of the new clock. The speed of the minute hand in the new clock is directly proportional to the digit it is going to approach. So, between 1 and 2, the speed is proportional to 2, and between 11 and 12, the speed is proportional to 12. The speed is the highest when the minute hand is between 11 and 12.

The speed of the minute hand in the new clock is the same as the speed of the minute hand in an ordinary clock when it is between 12 and 1. This means that the minute hand in the new clock will take the same amount of time to move from 12 to 1 as it would in an ordinary clock.

Let's calculate the time it takes for the minute hand in the new clock to move from 12 to 1. In an ordinary clock, the minute hand takes 60 minutes to complete one full revolution, which is from 12 to 12. So, the time it takes to move from 12 to 1 is 60/12 = 5 minutes.

Now, let's calculate the time it takes for the minute hand in the new clock to move from 12 to 1. The speed of the minute hand in the new clock is proportional to 12 when it is between 11 and 12. So, it will take 5 minutes for the minute hand to move from 11 to 12. Since the speed is proportional to the digit, it will take 5/12 minutes for the minute hand to move from 12 to 1.

Now, let's calculate the time in the new clock when the ordinary clock shows 9:30 am. In the ordinary clock, it takes 30 minutes for the minute hand to move from 12 to 6. Since the speed of the minute hand in the new clock is the same as the ordinary clock between 12 and 1, it will take the same amount of time for the minute hand in the new clock to move from 12 to 6.

So, the time in the new clock when the ordinary clock shows 9:30 am is 30 minutes.

Now, let's convert this time into hours and minutes. Since there are 60 minutes in an hour, the time in the new clock is 30/60 = 1/2 hour.

Therefore, the time in the new clock when the ordinary clock shows 9:30 am is 9:00 am + 1/2 hour = 9:30 am.
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Mr. Alaram designed a new clock, which has 12 divisions as usual, represented by the numbers 1 to 12. But the speed of the minute hand is directly proportional to the digit, which it is going to approach, i.e. if the minute hand is between 1 and 2, its speed is proportional to 2 and if it is between 11 and 12, its speed is proportional to 12. The speed of the minute hand, when it is between 12 and 1 is equal to that of an ordinary clock and both the clocks were set at 9 : 00 am.What will be the time in the ordinary clock, if the new clock shows 9 : 30 am?a)9 : 12 : 15 amb)9 : 20 : 15 amc)9 : 24 : 15 amd)9 : 30 : 15 amCorrect answer is option 'A'. Can you explain this answer?
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Mr. Alaram designed a new clock, which has 12 divisions as usual, represented by the numbers 1 to 12. But the speed of the minute hand is directly proportional to the digit, which it is going to approach, i.e. if the minute hand is between 1 and 2, its speed is proportional to 2 and if it is between 11 and 12, its speed is proportional to 12. The speed of the minute hand, when it is between 12 and 1 is equal to that of an ordinary clock and both the clocks were set at 9 : 00 am.What will be the time in the ordinary clock, if the new clock shows 9 : 30 am?a)9 : 12 : 15 amb)9 : 20 : 15 amc)9 : 24 : 15 amd)9 : 30 : 15 amCorrect answer is option 'A'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Mr. Alaram designed a new clock, which has 12 divisions as usual, represented by the numbers 1 to 12. But the speed of the minute hand is directly proportional to the digit, which it is going to approach, i.e. if the minute hand is between 1 and 2, its speed is proportional to 2 and if it is between 11 and 12, its speed is proportional to 12. The speed of the minute hand, when it is between 12 and 1 is equal to that of an ordinary clock and both the clocks were set at 9 : 00 am.What will be the time in the ordinary clock, if the new clock shows 9 : 30 am?a)9 : 12 : 15 amb)9 : 20 : 15 amc)9 : 24 : 15 amd)9 : 30 : 15 amCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Mr. Alaram designed a new clock, which has 12 divisions as usual, represented by the numbers 1 to 12. But the speed of the minute hand is directly proportional to the digit, which it is going to approach, i.e. if the minute hand is between 1 and 2, its speed is proportional to 2 and if it is between 11 and 12, its speed is proportional to 12. The speed of the minute hand, when it is between 12 and 1 is equal to that of an ordinary clock and both the clocks were set at 9 : 00 am.What will be the time in the ordinary clock, if the new clock shows 9 : 30 am?a)9 : 12 : 15 amb)9 : 20 : 15 amc)9 : 24 : 15 amd)9 : 30 : 15 amCorrect answer is option 'A'. Can you explain this answer?.
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