Question : P and Q can do a piece of work in 14 days. Q and R together can do it in 21 days. If P is twice as good a workman as R, then in how many days Q alone can do the work?
Option 1: 42 days
Option 2: 40 days
Option 3: 35 days
Option 4: 38 days
Correct Answer: 42 days
Solution :
Given: Number of days P and Q take to do a piece of work = 14 days
Number of days Q and R take to do a work = 21 days
P is twice as good as Workman as R
Let P, Q, and R can do the work in
Let the amount of work done by P, Q, and R in 1 day is
According to the question,
As per the condition given,
Putting the value in equation (1), and subtracting equation (2) from (1), we get
⇒
⇒
⇒
Putting the value of z in equation (2), we get:
⇒
⇒
⇒
Hence, the correct answer is 42 days.