P and Q working alone can complete a work in 9 days and 18 days respectively. They work on alternate days one at a time. P works on the first day. In how many days the whole work will be completed?
12
Take total work as the LCM of the two times so the daily rates are whole numbers: \(\text{LCM}(9,18) = 18\) units.
P finishes in 9 days, so P's rate \(= \dfrac{18}{9} = 2\) units/day; Q finishes in 18 days, so Q's rate \(= \dfrac{18}{18} = 1\) unit/day.
They alternate starting with P, so one full 2-day cycle (P then Q) does \(2 + 1 = 3\) units.
After 5 cycles = 10 days, work done \(= 5 \times 3 = 15\) units, leaving \(18 - 15 = 3\) units.
Day 11 is P's turn: \(15 + 2 = 17\) units. Day 12 is Q's turn: \(17 + 1 = 18\) units — the work is exactly complete.
Key idea: fix a convenient total, group alternate days into cycles, then finish the remainder day by day. The whole work is completed in 12 days.
Similar Questions
P, Q and R working alone can complete a work in 24, 30 and 40 days respectively. All three of them started the work together but after 8 days P left the work. Q left the work 6 days before the work was completed. R completed the remaining work alone. In how many days was the total work completed?
A does 60% of the work in 18 days. He then calls in B, and they together finish the remaining work in 4 days. How long would B alone take to do the whole work?
If 8 men can do a piece of work in 14 days, the time taken by 12 men to do the same piece of work will be:
A and B together can do a job in 6 days. A alone does it in 9 days. In how many days can B alone do it?
A can do a job in 10 days and B in 12 days. They work on alternate days starting with A. In how many days will the job be finished?
Aditya is twice as good a workman as Bipin and therefore can finish a job in 30 days less than Bipin. How many days are required to complete the job if working together?
A can do a piece of work in 20 days and B in 30 days. They work together for 5 days. How much work is left?
A alone can do a work in 20 days, B alone in 30 days. They work together for 6 days, then A leaves. How many more days will B take to finish the remaining work?
A can do a work in 18 days, B in 27 days. They start together, but after 6 days A leaves. In how many more days will B finish the remaining work?
Given ,6 men and 8 boys can complete the task in 10 days, and 26 men and 48 boys can finish it in just 2 days, how long will it take for 15 men and 20 boys to do the same work?
Important Questions from Time and Work
Mohan can do a piece of work in 10 days and Sohan in 15 days. They started working together, but after 3 days Mohan left the work . What time will Sohan take to finish the work?
A tank is filled in 8 hours by three taps A, B and C. The tap C is thrice as fast as B and B is twice as fast as A. How much time will pipe B alone take to fill the tank?
Had been one menless, then the number of days required to do a piece of work would have been one more. If the number of Man. Days required to complete the work is 56, how many workers were there?
A can do a piece of work in 16 hours, B and C can do it in 8 hours while A and C can do it 12 hours. How long will B alone take to do it?
- lf 12 men can do a work in 20 days, in how many days will the work be done by 15 men-
