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The quarter of the time from midnight to present time added to the half of the time from the present to midnight gives the present time. What is the present time?
- a)9 hrs past 36 minutes AM
- b)9 hrs past 34 minutes AM
- c)9 hrs past 38 minutes AM
- d)9 hrs past 32 minutes AM
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The quarter of the time from midnight to present time added to the hal...
Suppose present time= X
Time remaining till midnight = 24 - X
Therefore. according to question:
One quarter of present time = X/4
Half of remaining time till midnight = (24-X)/2
So,
(X/4) + {(24-X)/2} = X
(X + 48 - 2X) = 4X
48 = 5X
X = 48/5 = 9.6
So, present time is 9.6 hours or 9 hours 36 minutes or 9:36AM
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Community Answer
The quarter of the time from midnight to present time added to the hal...
The given problem states that the quarter of the time from midnight to the present time added to half of the time from the present to midnight gives the present time. We need to determine the present time based on this information.
Let's break down the problem into smaller parts to solve it step-by-step.
1. Determine the time from midnight to the present time.
The time from midnight to the present time is the time that has already passed. Since the problem does not provide the specific present time, we can consider it as X hours and Y minutes. Therefore, the time from midnight to the present time can be represented as X hours + Y minutes.
2. Determine the time from the present to midnight.
The time from the present to midnight is the time remaining until midnight. Since 24 hours make a day, the time from the present to midnight can be represented as 24 hours - X hours - Y minutes.
3. Formulate the equation.
According to the problem, the quarter of the time from midnight to the present time added to half of the time from the present to midnight gives the present time. Mathematically, this can be represented as:
(X hours + Y minutes)/4 + (24 hours - X hours - Y minutes)/2 = X hours + Y minutes
4. Solve the equation.
Let's solve the equation step-by-step:
(X/4) hours + (Y/4) minutes + (24 - X)/2 hours + (24 - Y)/2 minutes = X hours + Y minutes
Multiplying through by the common denominator 4, we get:
X hours + Y minutes + 2(24 - X) hours + 2(24 - Y) minutes = 4X hours + 4Y minutes
Simplifying the equation, we have:
X + Y + 48 - 2X + 48 - 2Y = 4X + 4Y
Combining like terms, we get:
96 - X - Y = 4X + 4Y
Rearranging the equation, we have:
5X + 5Y = 96
Dividing both sides by 5, we get:
X + Y = 19.2
Since X represents the hours and Y represents the minutes, we need to convert the decimal part of 0.2 into minutes. Multiplying 0.2 by 60, we get 12 minutes. Therefore, X + Y = 19 hours + 12 minutes.
5. Determine the present time.
The present time is X hours + Y minutes, which is 19 hours + 12 minutes. This can be written as 19:12 or 19 hours past 12 minutes AM.
Therefore, the correct answer is option A) 9 hours past 36 minutes AM.
Let's break down the problem into smaller parts to solve it step-by-step.
1. Determine the time from midnight to the present time.
The time from midnight to the present time is the time that has already passed. Since the problem does not provide the specific present time, we can consider it as X hours and Y minutes. Therefore, the time from midnight to the present time can be represented as X hours + Y minutes.
2. Determine the time from the present to midnight.
The time from the present to midnight is the time remaining until midnight. Since 24 hours make a day, the time from the present to midnight can be represented as 24 hours - X hours - Y minutes.
3. Formulate the equation.
According to the problem, the quarter of the time from midnight to the present time added to half of the time from the present to midnight gives the present time. Mathematically, this can be represented as:
(X hours + Y minutes)/4 + (24 hours - X hours - Y minutes)/2 = X hours + Y minutes
4. Solve the equation.
Let's solve the equation step-by-step:
(X/4) hours + (Y/4) minutes + (24 - X)/2 hours + (24 - Y)/2 minutes = X hours + Y minutes
Multiplying through by the common denominator 4, we get:
X hours + Y minutes + 2(24 - X) hours + 2(24 - Y) minutes = 4X hours + 4Y minutes
Simplifying the equation, we have:
X + Y + 48 - 2X + 48 - 2Y = 4X + 4Y
Combining like terms, we get:
96 - X - Y = 4X + 4Y
Rearranging the equation, we have:
5X + 5Y = 96
Dividing both sides by 5, we get:
X + Y = 19.2
Since X represents the hours and Y represents the minutes, we need to convert the decimal part of 0.2 into minutes. Multiplying 0.2 by 60, we get 12 minutes. Therefore, X + Y = 19 hours + 12 minutes.
5. Determine the present time.
The present time is X hours + Y minutes, which is 19 hours + 12 minutes. This can be written as 19:12 or 19 hours past 12 minutes AM.
Therefore, the correct answer is option A) 9 hours past 36 minutes AM.
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