# Time and Work

1. Anil alone can complete a work in 10 days while Bikash alone can complete it in 15 days. In how many days can they together complete the same work?

A. 4 days

B. 5 days

C. 6 days

D. 8 days

Explanation:

Let total work = LCM (10,15) = 30 unit
In 1 day, Anil does 3 unit work.
In 1 day, Bikash does 2 unit work.
In 1 day, both does 5 units of work.
So, Number of days required to complete the work together = 30/5 = 6 days

2. Amit can do a work in 15 days and Bishnu in 20 days. If they work on it together for 4 days, then the fraction of the work that left is:

A. 1/3

B. 1/2

C. 7/15

D. 8/15

Explanation:

Let total work = LCM (15,20) = 60 unit
In 1 day, Amit does 4 unit work.
In 1 day, Bishnu does 3 unit work.
In 4 day, both does 4 x (4 + 3) = 28 units of work.
So, fraction of work remaining = (60 - 28)/60 = 32/60 = 8/15

3. Ashish can finish a work in 18 days and Biswas can finish it in half the time taken by Ashish. Then, working together, what part of the same work they can finish in a day?

A. 1/6

B. 1/9

C. 2/5

D. 2/7

Explanation:

Biswas takes 9 days to finish the work.
Let total work = LCM (18,9) = 18 unit
In 1 day, Ashish does 1 unit work.
In 1 day, Biswas does 2 unit work.
In 1 day, both does (1 + 2) = 3 units of work.
So, fraction of work completed = 3/18 = 1/6

4. A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B left and the remaining work was completed by A alone. The whole work was completed in

A. 8 days

B. 10 days

C. 12 days

D. 15 days

Explanation:

Let total work = LCM (15,10) = 30 unit
In 1 day, A does 2 unit work.
In 1 day, B does 3 unit work.
In 2 day, both does 2 x (2 + 3) = 10 units of work.
Remaining work = 30 - 10 = 20 unit
Time taken by A to complete it = 20/2 = 10 days
Total time for work completion = 2 + 10 = 12 days

5. Amit and Bishnu can do a piece of work in 12 days and 16 days respectively. Both work together for 3 days and then Amit left. How long will Bishnu take to complete the remaining work?

A. 15 days

B. 12 days

C. 10 days

D. 9 days