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One day, Rahul started a work at 9 AM and Gautam joined him two hours later. They then worked together and completed the work at 5 PM the same day. If both had started at 9 AM and worked together, the work would have been completed 30 minutes earlier. Working alone, the time Rahul would have taken, in hours, to complete the work is    [2021]
  • a)
     11.5
  • b)
     10
  • c)
     12.5
  • d)
     12
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
One day, Rahul started a work at 9 AM and Gautam joined him two hours ...
Let Rahul work at a units/hr and Gautam at b units/hour
Now as per the condition :
8a + 6b =7.5a + 7.5b
so we get 0.5a = 1.5b
or a = 3b
Therefore total work = 8a + 6b = 8a + 2a = 10a
Now Rahul alone takes 10a/10 = 10 hours.
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Community Answer
One day, Rahul started a work at 9 AM and Gautam joined him two hours ...
Given Information:
- Rahul started work at 9 AM
- Gautam joined him 2 hours later
- They completed the work at 5 PM
- If they both started at 9 AM, the work would have been completed 30 minutes earlier

Calculating Time Taken:
Let's assume Rahul takes x hours to complete the work alone.
So, Gautam takes x-2 hours to complete the work alone.
Together, they complete the work in 8 hours (from 9 AM to 5 PM).
If they had started together at 9 AM, the work would have been completed in 7.5 hours (30 minutes earlier).
So, Rahul and Gautam's combined work rate is:
1/8 + 1/(x-2) = 1/7.5
Solving this equation, we get x = 10 hours.
Therefore, Rahul would take 10 hours to complete the work alone.

Final Answer:
The time Rahul would have taken, in hours, to complete the work alone is 10 hours (option B).
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One day, Rahul started a work at 9 AM and Gautam joined him two hours later. They then worked together and completed the work at 5 PM the same day. If both had started at 9 AM and worked together, the work would have been completed 30 minutes earlier. Working alone, the time Rahul would have taken, in hours, to complete the work is [2021]a)11.5b)10c)12.5d)12Correct answer is option 'B'. Can you explain this answer?
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