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Mani and Hari can do a work alone in 40 days and 60 days respectively. Both start the work together and after 6 days, Mani increases his efficiency by 40% while Hari decreases his efficiency by 10%. Then the work will be delayed/completed early by how many days?
  • a)
    0.5 days
  • b)
    1.5 days
  • c)
    1 day
  • d)
    2 days
  • e)
    None of these
Correct answer is option 'E'. Can you explain this answer?
Most Upvoted Answer
Mani and Hari can do a work alone in 40 days and 60 days respectively...
Here's the detailed explanation for the given question:

Given:
- Mani can complete the work alone in 40 days.
- Hari can complete the work alone in 60 days.

Step 1: Calculate their daily efficiency
- Mani's daily efficiency = 1/40 = 0.025 (work done per day)
- Hari's daily efficiency = 1/60 = 0.0167 (work done per day)

Step 2: Calculate the work done in 6 days
- Mani's work done in 6 days = 6 * 0.025 = 0.15
- Hari's work done in 6 days = 6 * 0.0167 = 0.1

Step 3: Calculate the remaining work
- Remaining work = 1 - (0.15 + 0.1) = 0.75

Step 4: Calculate the new efficiencies
- Mani's increased efficiency = 0.025 + (40% * 0.025) = 0.025 + 0.01 = 0.035
- Hari's decreased efficiency = 0.0167 - (10% * 0.0167) = 0.0167 - 0.00167 = 0.01503

Step 5: Calculate the time taken to complete the remaining work
- Time taken by Mani = 0.75 / 0.035 = 21.43 days (approximately)
- Time taken by Hari = 0.75 / 0.01503 = 49.93 days (approximately)

Step 6: Calculate the total time taken to complete the work
- Total time taken = 6 + 21.43 = 27.43 days (approximately)

Step 7: Calculate the delay/completion
- Delay/completion = 40 - 27.43 = 12.57 days (approximately)

Therefore, the work will be delayed/completed early by approximately 12.57 days.
Since none of the given options match this value, the correct answer is "None of these" (option E).
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Community Answer
Mani and Hari can do a work alone in 40 days and 60 days respectively...
Let the total work be LCM of 40 and 60 = 120 units
Mani alone do =120/40 = 3 units of work in a day.
Hari alone do =120/60 = 2 units of work in a day.
Original time taken to complete the work = 120/5 = 24 days.
Units of work done in 6 days = 6 × 5 = 30 units
Increased efficiency of Mani = 3 × 1.4 = 4.2 units/day
Decreased efficiency of Hari = 2 × 0.9 = 1.8 units/day
Remaining work = 120 - 30 = 90 units
90 units of work done in = 90/6 = 15 days
Total time taken = 15 + 6 = 21 days
So, the work will be completed 3 days earlier to complete.
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Mani and Hari can do a work alone in 40 days and 60 days respectively. Both start the work together and after 6 days, Mani increases his efficiency by 40% while Hari decreases his efficiency by 10%. Then the work will be delayed/completed early by how many days?a)0.5 daysb)1.5 daysc)1 dayd)2 dayse)None of theseCorrect answer is option 'E'. Can you explain this answer?
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