1. Calculate total minutes required to count 1 billion:
Total numbers to count = 1,000,000,000
Rate of counting = 200 per minute
Total minutes=2001,000,000,000=5,000,000 minutes
2. Convert minutes into hours and days:
Total hours=605,000,000=83,333 hours and 20 minutes
Total days=2483,333=3,472 days and 5 hours
So, the net counting time is 3,472 days, 5 hours, and 20 minutes.
3. Account for Leap Years and "Days Off":
The start date is 1 January 2001. We need to find how many years are in 3,472 days.
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In a standard 4-year cycle (e.g., 2001-2004), there are 365×3+366=1,461 days.
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However, the question states you get a day off every four years. Since leap years occur every four years, this "day off" essentially cancels out the extra day added by the leap year (Feb 29).
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Therefore, for calculation purposes, every year effectively has 365 days.
4. Calculate Years:
Number of years=3653,472
This gives us 9 years and 187 days.
5. Final Result:
Combining all the units calculated:
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Years: 9
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Days: 187
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Hours: 5
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Minutes: 20
Total time = 9 yr, 187 days, 5 h, 20 min
Final Answer:
The correct option is (c) 9 yr, 187 days, 5 h, 20 min.
