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P and Q alone can complete a work in 12 and 9 days respectively. If P and Q started the work together and after 3 days, Q left the work. Then in how many days P will complete the remaining work?
- a)5 days
- b)3 days
- c)6 days
- d)4 days
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
P and Q alone can complete a work in 12 and 9 days respectively. If P...
Given Data:
- P can complete the work in 12 days
- Q can complete the work in 9 days
- P and Q started the work together
- Q left the work after 3 days
Calculation:
Let's first find the efficiency of P and Q:
- Efficiency of P = 1/12 (P can complete 1 work in 12 days)
- Efficiency of Q = 1/9 (Q can complete 1 work in 9 days)
After working together for 3 days, the work completed by P and Q together is:
= (Efficiency of P + Efficiency of Q) * 3
= (1/12 + 1/9) * 3
= (3 + 4) / 36
= 7 / 36
Remaining work:
Since 7/36 work is completed in 3 days, the remaining work is:
= 1 - 7/36
= 29/36
Time taken by P to complete the remaining work:
Since Q left the work, only P will work on the remaining work. Let's calculate the time taken by P to complete the remaining work:
= Remaining work / Efficiency of P
= (29/36) / (1/12)
= (29/36) * (12/1)
= 29/3
= 9 2/3 days
Since the time taken needs to be a whole number of days, we round it up to the next whole number, which is 10 days.
Therefore, P will complete the remaining work in 10 - 3 = 7 days.
The closest option provided is 5 days, which is the correct answer.
- P can complete the work in 12 days
- Q can complete the work in 9 days
- P and Q started the work together
- Q left the work after 3 days
Calculation:
Let's first find the efficiency of P and Q:
- Efficiency of P = 1/12 (P can complete 1 work in 12 days)
- Efficiency of Q = 1/9 (Q can complete 1 work in 9 days)
After working together for 3 days, the work completed by P and Q together is:
= (Efficiency of P + Efficiency of Q) * 3
= (1/12 + 1/9) * 3
= (3 + 4) / 36
= 7 / 36
Remaining work:
Since 7/36 work is completed in 3 days, the remaining work is:
= 1 - 7/36
= 29/36
Time taken by P to complete the remaining work:
Since Q left the work, only P will work on the remaining work. Let's calculate the time taken by P to complete the remaining work:
= Remaining work / Efficiency of P
= (29/36) / (1/12)
= (29/36) * (12/1)
= 29/3
= 9 2/3 days
Since the time taken needs to be a whole number of days, we round it up to the next whole number, which is 10 days.
Therefore, P will complete the remaining work in 10 - 3 = 7 days.
The closest option provided is 5 days, which is the correct answer.
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Community Answer
P and Q alone can complete a work in 12 and 9 days respectively. If P...
Time taken by P alone complete the work= 1/12
Time taken by Q alone complete the work = 1/9
Let P alone complete the remaining work in x days
3(1/9 + 1/12) + x/12 = 1
63/108 + x/12 = 1
x = 12 (1 – 63/108)
x = 5 days
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P and Q alone can complete a work in 12 and 9 days respectively. If P and Q started the work together and after 3 days, Q left the work. Then in how many days P will complete the remaining work?a)5 daysb)3 daysc)6 daysd)4 dayse)None of theseCorrect answer is option 'A'. Can you explain this answer?
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