NIMCET 2009 — Reasoning PYQ

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Question

NIMCET 2009 — Reasoning PYQ

NIMCET | Reasoning | 2009

How long would it take you to count 1 billion orally if you could count 200 every minute and were given a day off every four years? Assume that you start counting on 1 January 2001.

Choose the correct answer:

Explanation

1. Calculate total minutes required to count 1 billion:

Total numbers to count = $1,000,000,000$

Rate of counting = $200$ per minute

\text{Total minutes} = \frac{1,000,000,000}{200} = 5,000,000 \text{ minutes}

2. Convert minutes into hours and days:

\text{Total hours} = \frac{5,000,000}{60} = 83,333 \text{ hours and } 20 \text{ minutes}

\text{Total days} = \frac{83,333}{24} = 3,472 \text{ days and } 5 \text{ 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.

In a standard 4-year cycle (e.g., 2001-2004), there are $365 \times 3 + 366 = 1,461$ days.
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).
Therefore, for calculation purposes, every year effectively has 365 days.

4. Calculate Years:

\text{Number of years} = \frac{3,472}{365}

3,472 = (365 \times 9) + 187

3,472 = 3,285 + 187

This gives us 9 years and 187 days.

5. Final Result:

Combining all the units calculated:

Years: $9$
Days: $187$
Hours: $5$
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.