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Ramesh and Ganesh can together complete a work in 16 days. After seven days of working together, Ramesh got sick and his efficiency fell by 30%. As a result, they completed the work in 17 days instead of 16 days. If Ganesh had worked alone after Ramesh got sick, in how many days would he have completed the remaining work?
(CAT 2018)
  • a)
    13.5
  • b)
    11
  • c)
    12
  • d)
    14.5
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Ramesh and Ganesh can together complete a work in 16 days. After seven...
Let r and g be the rates of work of Ramesh and Ganesh respectively.
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Ramesh and Ganesh can together complete a work in 16 days. After seven...
Given:
- Ramesh and Ganesh can complete the work together in 16 days.
- After 7 days of working together, Ramesh's efficiency fell by 30%.
- They completed the work in 17 days instead of the expected 16 days.

To find:
The number of days Ganesh would have taken to complete the remaining work if he had worked alone after Ramesh got sick.

Solution:

Let's assume the total work to be done is 1 unit.

Efficiency of Ramesh and Ganesh together:
- In 16 days, they complete the work together, so their combined efficiency is 1/16 unit per day.
- Therefore, Ramesh's efficiency is (1/16) - (30% of 1/16) = (1/16) - (3/160) = 7/160 unit per day.

Work done by Ramesh and Ganesh in 7 days:
- Ramesh and Ganesh work together for 7 days, so the work done by them is 7 * (1/16) = 7/16 unit.

Remaining work:
- The remaining work is 1 - (7/16) = 9/16 unit.

Work done by Ramesh and Ganesh after Ramesh got sick:
- Ramesh's efficiency decreased by 30% after he got sick, so his new efficiency is (7/160) * 70% = 7/228 unit per day.
- Ganesh's efficiency remains the same, i.e., 1/16 unit per day.
- Let's assume Ganesh takes 'x' days to complete the remaining work alone.

Equation:
- Work done by Ramesh after getting sick + Work done by Ganesh = Remaining work
- (7/228) * (17-7) + (1/16) * x = 9/16

Solving the equation:
- (7/228) * 10 + (1/16) * x = 9/16
- (7/228) * 10 + (1/16) * x = 9/16
- (35/1140) + (1/16) * x = 9/16
- (1/32) + (1/16) * x = 9/16
- (1/16) * x = 9/16 - 1/32
- (1/16) * x = 18/32 - 1/32
- (1/16) * x = 17/32
- x = (17/32) * 16
- x = 8.5

Therefore, Ganesh would have taken 8.5 days to complete the remaining work alone.
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