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P and Q together can complete the job in 20 days. Both started the work together and after 8 days, P worked at 80% of his efficiency and Q worked at 2/3rd of its efficiency so the remaining work completed in 4 days more than the stipulated time. If after 8 days only slower worker worked with his original efficiency then in how many days remaining work will be completed?
  • a)
    36 days
  • b)
    28 days
  • c)
    40 days
  • d)
    32 days
  • e)
    None of these
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
P and Q together can complete the job in 20 days. Both started the wo...
Let the efficiency of P and Q = a, and b respectively
After 8 days, if they both worked with original efficiency then the remaining work completed in 12 days, but after 8 days when they worked with their reduced efficiency, so they completed the remaining work in 16 days.
Now,
(a + b) x 12 = (80% x a + 2/3 x b) x 16
3a + 3b = 16a/5 + 8b/3
So, b/3 = a/5
So, a/b = 5/3
After 8 days amount of work remaining = 12 x (5 + 3) = 96 units
Time taken by Q to complete the remaining work = 96/3 = 32 days
Hence answer is option D
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Community Answer
P and Q together can complete the job in 20 days. Both started the wo...
Understanding the Problem:
- Let the total work be 1 unit.
- P and Q together complete the job in 20 days.
- After 8 days, P worked at 80% efficiency and Q worked at 2/3 efficiency.
- Remaining work was completed in 4 days more than the stipulated time.

Calculating Efficiencies:
- Since P and Q together complete the job in 20 days, their combined efficiency is 1/20.
- Let P's efficiency be x and Q's efficiency be y.
- Therefore, x + y = 1/20.

Calculating Work Done:
- In the first 8 days, P and Q together completed 8*(x+y) = 8/20 = 2/5 of the work.
- So, the remaining work is 1 - 2/5 = 3/5.

Calculating Work Done in the Next 4 Days:
- After 8 days, P worked at 80% efficiency and Q worked at 2/3 efficiency.
- So, the work done by P in the next 4 days = 4 * 0.8 * x = 3.2x.
- The work done by Q in the next 4 days = 4 * (2/3) * y = 8/3y.
- Combined work done by P and Q in the next 4 days = 3.2x + 8/3y.

Formulating Equations:
- Since the remaining work was completed in 4 days more than the stipulated time, the work done in the next 4 days equals the remaining work.
- Therefore, 3.2x + 8/3y = 3/5.

Solving the Equations:
- Substitute x + y = 1/20 into the equation 3.2x + 8/3y = 3/5.
- Solve for x and y.
- Once you have x and y, calculate how many more days the slower worker (Q) will take to complete the remaining work.
Therefore, the correct answer is option 'D' - 32 days.
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P and Q together can complete the job in 20 days. Both started the work together and after 8 days, P worked at 80% of his efficiency and Q worked at 2/3rd of its efficiency so the remaining work completed in 4 days more than the stipulated time. If after 8 days only slower worker worked with his original efficiency then in how many days remaining work will be completed?a)36 daysb)28 daysc)40 daysd)32 dayse)None of theseCorrect answer is option 'D'. Can you explain this answer?
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