Ques 1 Time and Work
If A and B together can complete a work 18 days, A and C together in 12 days, and B and C together in 9 days, then B alone can do the work in?
(A + B)'s one day work = 1/18.
(A + C)'s one day work = 1/12.
(B + C)'s one day work = 1/9.
Adding all three equations and dividing by 2.
2(A + B + C)'s one day work = (1/18) + (1/12) + (1/9) = 1/8.
B's one day work = (A + B + C)'s one day work - (A + C)'s one day work.
= 1/8 - 1/12 = 1/24.
Therefore, B alone can complete the work in 24 days.
Ques 2 Time and Work
A can complete a task in 6 days, while B can complete the same task in 12 days. How many days will they take to complete the same task if they work together?
A's one day work = 1/6.
B's one day work = 1/12.
(A + B)'s one day work = (1/6) + (1/12) = 1/4.
Time to complete the work together = 1 / (1/4) = 4 days.
Ques 3 Time and Work
A can complete one-sixth of a work in 5 days and B can complete one-fourth of the same work in 15 days. In how many days, will both working together complete the work?
A can do 1/6 of the job in 5 days, so he can finish the whole job in 30 days (6 x 5).
B can do 1/4 of the job in 15 days, so he can finish the whole job in 60 days (4 x 15).
When they work together, they do more work each day.
A does 1/30 of the job in a day.
B does 1/60 of the job in a day.
Together, they do 1/30 + 1/60 = 1/20 of the job in a day.
So, they will finish the whole job in 20 days.
Ques 4 Time and Work
15 persons working 6 hours per day earn ₹900. How much money will 20 persons earn, working 10 hours per day?
Ques 5 Time and Work
A pipe is filling a tank of 200 litres capacity at 5 litres/hr. Because of a leak it takes 80 hours more to fill the tank. What is the rate in litres/hr at which the water is leaking?