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P, Q and R can do a piece of work in 16, 24 and 30 days respectively. They started the work simultaneously but P stops the work after 4 days and Q called off the work 2 days before the completion. In what time the work is finished?
- a)100/9 days
- b)100/11 days
- c)100/7 days
- d)100/13 days
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
P, Q and R can do a piece of work in 16, 24 and 30 days respectively. ...
4/16 + (T -2)/24 + T/30 = 1 where T is the time taken to complete the job
Most Upvoted Answer
P, Q and R can do a piece of work in 16, 24 and 30 days respectively. ...
To find the time taken to complete the work, we need to calculate the work done per day by each person.
Let's denote the work done by P, Q, and R per day as Pd, Qd, and Rd respectively.
Given:
P completes the work in 16 days, so Pd = 1/16 (as 1 work is done in 16 days)
Q completes the work in 24 days, so Qd = 1/24 (as 1 work is done in 24 days)
R completes the work in 30 days, so Rd = 1/30 (as 1 work is done in 30 days)
Let's assume the total work to be done is 1 unit.
Work done by P in 4 days = Pd * 4 = (1/16) * 4 = 1/4
Remaining work = 1 - 1/4 = 3/4
Now, Q called off the work 2 days before completion, which means Q worked for (24 - 2) = 22 days.
Work done by Q in 22 days = Qd * 22 = (1/24) * 22 = 11/12
Remaining work = 3/4 - 11/12 = 9/12 - 11/12 = -2/12 = -1/6
The negative value indicates that the work is already completed before Q called off the work.
Since R was working until the completion of the work, R worked for a total of 30 days.
Work done by R in 30 days = Rd * 30 = (1/30) * 30 = 1
Therefore, the work is already completed when Q called off the work.
The remaining work is negative, indicating that the work is already finished.
Hence, the work is finished in 22 days.
Therefore, the correct answer is option A) 100/9 days.
Let's denote the work done by P, Q, and R per day as Pd, Qd, and Rd respectively.
Given:
P completes the work in 16 days, so Pd = 1/16 (as 1 work is done in 16 days)
Q completes the work in 24 days, so Qd = 1/24 (as 1 work is done in 24 days)
R completes the work in 30 days, so Rd = 1/30 (as 1 work is done in 30 days)
Let's assume the total work to be done is 1 unit.
Work done by P in 4 days = Pd * 4 = (1/16) * 4 = 1/4
Remaining work = 1 - 1/4 = 3/4
Now, Q called off the work 2 days before completion, which means Q worked for (24 - 2) = 22 days.
Work done by Q in 22 days = Qd * 22 = (1/24) * 22 = 11/12
Remaining work = 3/4 - 11/12 = 9/12 - 11/12 = -2/12 = -1/6
The negative value indicates that the work is already completed before Q called off the work.
Since R was working until the completion of the work, R worked for a total of 30 days.
Work done by R in 30 days = Rd * 30 = (1/30) * 30 = 1
Therefore, the work is already completed when Q called off the work.
The remaining work is negative, indicating that the work is already finished.
Hence, the work is finished in 22 days.
Therefore, the correct answer is option A) 100/9 days.
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P, Q and R can do a piece of work in 16, 24 and 30 days respectively. They started the work simultaneously but P stops the work after 4 days and Q called off the work 2 days before the completion. In what time the work is finished?a)100/9 daysb)100/11 daysc)100/7 daysd)100/13 dayse)None of theseCorrect answer is option 'A'. Can you explain this answer?
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