P and Q together can complete a job in 90days, Q and R takes 60 days to complete the same work and P and R will take 45 days to complete the same work. How much time will P, Q and R will take to complete the work together.a)40 daysb)42 daysc)36 daysd)44 dayse)None of theseCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

(1/90 + 1/60 + 1/45)*1/2 = (1/P +1/Q + 1/R) = 1/40
so 40 days

Answer

TOTAL WORK =180
UNIT WORK = 4.5
TOTAL DAY =180÷4.5
40

Answer

To solve this problem, we can use the concept of work done per day. Let's assume that P, Q, and R can complete the work in x days when working together.

Given information:
1. P and Q together can complete the job in 90 days.
2. Q and R together can complete the job in 60 days.
3. P and R together can complete the job in 45 days.

From the given information, we can derive the following equations:

1. (P + Q) completes 1 job in 90 days.
2. (Q + R) completes 1 job in 60 days.
3. (P + R) completes 1 job in 45 days.

Let's calculate the work done per day (W) for each pair:

1. Work done per day by P and Q = 1/90
2. Work done per day by Q and R = 1/60
3. Work done per day by P and R = 1/45

To find the work done per day by P, Q, and R working together, we add up the individual work done per day:

Work done per day by P, Q, and R = W(P) + W(Q) + W(R)

Now, let's find the value of W(P), W(Q), and W(R) using the given information:

1. W(P) + W(Q) = 1/90
2. W(Q) + W(R) = 1/60
3. W(P) + W(R) = 1/45

Adding equations 1, 2, and 3, we get:

2(W(P) + W(Q) + W(R)) = 1/90 + 1/60 + 1/45
2(W(P) + W(Q) + W(R)) = 3/180 + 2/180 + 4/180
2(W(P) + W(Q) + W(R)) = 9/180
W(P) + W(Q) + W(R) = 9/360
W(P) + W(Q) + W(R) = 1/40

Therefore, P, Q, and R working together can complete 1 job in 40 days.

Hence, the correct answer is option A) 40 days.

Similar Quant Doubts

To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it?

A does half as much work as B does in one sixth of the time. If together they take 20 days to complete the work, then what is the time taken by A to complete the work independently.

X takes 4 days to complete one-third of a job, Y takes 3 days to complete one-sixth of the same work and Z takes 5 days to complete half the job. If all of them work together for 3 days and X and Z quit, how long will it take for Y to complete the remaining work done.

A does half as much work as B does in one sixth of the time. If together they take 20 days to complete the work, then what is the time taken by B to complete the work independently.

Top Courses for Quant

Suggested Free Tests

Related Content

Quant Courses

Related Exams

Related Question Answers

Related Searches

Company