P can do a piece of work in 200 days. Q and R can do the same work in 100 days. P, Q, and R started the work together, and they worked together for 40 days. Q left the work, and P and R together finished the remaining work in 40 days. Find the number of days in which Q alone can do the total work.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 200 days.
P can do a piece of work = 200 days.
Q and R can do the same work = 100 days
Let's assume the total work = 200 unit
Efficiency of P = 200/200 = 1
Efficiency of Q + R = 200/100 = 2
According to the question,
P, Q, and R started the work together, and they worked together for 40 days.
Their 40 days work = (1 + 2) × 40 = 120
Remaining work = 200 - 120 = 80
It was finished by P and R in 40 days
80/(1 + R) = 40
R = 1
Q = 2 - 1 = 1
So, Q alone can do the total work = 200/1 = 200 days