Select the correct answerA, B and C can do a piece of work in 30 days, 45 days and 90 days, respectively. A starts the work and he is assisted by B and C together on every third day. In how many days will the work be completed?Options24233022

To solve this problem, we first need to find out the amount of work A, B, and C can do in a day.

1. A can complete the work in 30 days, so A can do 1/30 of the work in a day.
2. B can complete the work in 45 days, so B can do 1/45 of the work in a day.
3. C can complete the work in 90 days, so C can do 1/90 of the work in a day.

Now, let's calculate the work done by A, B, and C together in 3 days:

• On the first and second day, only A works, so the work done is 2 * (1/30) = 1/15.
• On the third day, A, B, and C all work, so the work done is (1/30) + (1/45) + (1/90) = 1/10.

So, in 3 days, they complete 1/15 + 1/10 = 1/6 of the work.

Now, we need to find out how many 3-day cycles it takes to complete the work. Since 1/6 of the work is done in 3 days, it will take 6 * 3 = 18 days to complete 1 whole work.

But, we need to check if the work is completed exactly at the end of the 18th day.

• On the 19th and 20th day, only A works, so the work done is 2 * (1/30) = 1/15.
• On the 21st day, A, B, and C all work, so the work done is (1/30) + (1/45) + (1/90) = 1/10.

So, in 3 more days, they complete 1/15 + 1/10 = 1/6 of the work.

Adding this to the work done in 18 days, we get 1 + 1/6 = 1 1/6. This is more than 1, which means the work is completed before the 21st day.

So, the work is completed sometime between the 18th and 21st day. Since the options are all whole numbers, the correct answer is 22 days.