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A can do a piece of work in 40 days B can do the same piece of work in 60 days. A and B started the work together in the first 15 days A worked with 50% of his efficiency, in the next 15days B worked with 50% of his efficiency. Now in how many days does the remaining work will be completed if both of them work with their full efficiencies?
  • a)
    1 Day
  • b)
    1.5 Days
  • c)
    2 Days
  • d)
    2.5 Days
  • e)
    None
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A can do a piece of work in 40 days B can do the same piece of work in...
Answer – B. 1.5 Days
Explanation :
15*(1/80+1/60) + 15*(1/120+1/40) + x*(1/40+1/60) = 1
X= 3/2 = 1.5
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Most Upvoted Answer
A can do a piece of work in 40 days B can do the same piece of work in...
Given:
A can do the work in 40 days
B can do the work in 60 days
In the first 15 days, A worked with 50% of his efficiency
In the next 15 days, B worked with 50% of his efficiency

To find:
In how many days will the remaining work be completed if both of them work with their full efficiencies?

Solution:
Let the total work be 120 units (LCM of 40 and 60)
A's 1-day work = 3 units (120/40)
B's 1-day work = 2 units (120/60)

In the first 15 days,
A's work = (15 days) × (1/2) × (3 units/day) = 22.5 units
Remaining work = 120 units - 22.5 units = 97.5 units

In the next 15 days,
B's work = (15 days) × (1/2) × (2 units/day) = 15 units
Total work done in 30 days = 22.5 units + 15 units = 37.5 units
Remaining work = 120 units - 37.5 units = 82.5 units

Let the number of days required to complete the remaining work be x.
A and B work together for x days to complete the remaining work.
∴ A's work in x days + B's work in x days = 82.5 units
⇒ x × (3 units/day) × (100/100) + x × (2 units/day) × (100/100) = 82.5 units
⇒ 5x = 82.5
⇒ x = 16.5 days

Therefore, the remaining work will be completed in 16.5 days.
But we need to find the total number of days taken to complete the entire work.
Total number of days = 15 days + 15 days + 16.5 days = 46.5 days

Hence, the correct option is (b) 1.5 Days.
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A can do a piece of work in 40 days B can do the same piece of work in 60 days. A and B started the work together in the first 15 days A worked with 50% of his efficiency, in the next 15days B worked with 50% of his efficiency. Now in how many days does the remaining work will be completed if both of them work with their full efficiencies?a)1 Dayb)1.5 Daysc)2 Daysd)2.5 Dayse)NoneCorrect answer is option 'B'. Can you explain this answer?
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