Question

Tilak, mukesh, and sonali can complete a work in 10, 12 and 15 days respectively. all three agree to complete the work together. after 2 days, tilak leaves the work. mukesh left the job 3 days before the completion of the work. sonali alone continues until the work got completed. how many days did it take to complete the task?

A. 4
B. 5
C. 7
D. 8

Answer 1

Tilak, Mukesh, and Sonali work together for 2 days, then Tilak leaves and Mukesh and Sonali work for another 2 days before Mukesh departs. Sonali works alone for the last 3 days. The total time taken to complete the work is 7 days.

Step-by-step explanation:

To solve the problem of how many days it takes Tilak, Mukesh, and Sonali to complete the work, we need to calculate the work done by each member every day and then establish the total time taken for the completion of the work.

First, we find the individual work rates:

Tilak can complete the work in 10 days, so he does 1/10 of the work per day.

Mukesh can complete the work in 12 days, so he does 1/12 of the work per day.

Sonali can complete the work in 15 days, so she does 1/15 of the work per day.

When they work together for the first 2 days, they complete (1/10 + 1/12 + 1/15) of the work each day. Calculating the least common multiple (LCM) of 10, 12, and 15, which is 60, their combined work for each day is 6/60 + 5/60 + 4/60 = 15/60 or 1/4 of the work per day.

So in 2 days, they complete 2 * 1/4 = 1/2 of the work.

Now Tilak leaves, and Mukesh and Sonali work together for the next few days. Their daily work is now 1/12 + 1/15 = 9/60 or 3/20 of the work per day.

Mukesh then leaves 3 days before the completion, so we only have Sonali's rate at 1/15 per day to finish the remaining work. If x is the total number of days taken to complete the work, Sonali must have worked alone for (x - 2) - (x - 2 - 3) = 3 days.

Let's calculate the portion of work Sonali completes alone:

3 days * 1/15 per day = 3/15 = 1/5 of the work.

We now know that 1/2 of the work was completed in the first two days, and Sonali completes an additional 1/5 alone. Together, Mukesh and Sonali must have completed the remaining work in the period between.

The remaining work after the first two days is 1 - 1/2 = 1/2. The work Sonali completes alone is subtracted from this, leaving 1/2 - 1/5 = 5/10 - 2/10 = 3/10 of the work to be done by Mukesh and Sonali together.

At their combined rate of 3/20 per day, it takes them (3/10) / (3/20) = 2 days to complete the remaining 3/10.

Adding all the parts together, the task is completed in 2 (initial days with Tilak) + 2 (Mukesh and Sonali) + 3 (Sonali alone) = 7 days.

Therefore, the task took 7 days to complete, which is option C.

Answer 2

It took 6 days to complete the work when Tilak, Mukesh, and Sonali worked together under the given conditions, with Tilak leaving after 2 days and Mukesh leaving 3 days before the end. The correct answer is B. 5.

Step-by-step explanation:

To solve this problem, we need to determine the work rates of Tilak, Mukesh, and Sonali and figure out how much work each can complete per day. Then, we can calculate how many days it will take for all the work to be finished with the given conditions.

Tilak can complete the work in 10 days, which means Tilak's work rate is 1/10 of the work per day. Mukesh can complete the work in 12 days, so Mukesh's work rate is 1/12 of the work per day. Sonali can complete the work in 15 days, meaning Sonali's work rate is 1/15 of the work per day.

Working together for 2 days, all three complete 2*(1/10 + 1/12 + 1/15) of the work. This simplifies to 2*(1/10 + 1/12 + 1/15) = 2*(6/60 + 5/60 + 4/60) = 2*(15/60) = 1/2 of the work.

After this, Tilak leaves, and Mukesh and Sonali work together for the next (x - 3) days, where x is the total number of days taken to complete the work. During this time, they complete (x - 3)*(1/12 + 1/15) = (x - 3)*(27/180) = (x - 3)*(3/20) of the work.

For the last 3 days, only Sonali is working, completing 3*(1/15) = 3/15 = 1/5 of the work.

Combining all portions completed, we have 1/2 + (x - 3)*(3/20) + 1/5 = 1 (the whole work). Simplifying and solving for x gives us x = 6 days.

Therefore, it took 6 days to complete the work, making Option B the correct answer.