S alone can do a piece of work in 14 days. T alone can do the same work in 21 days. U alone can do the same work in 28 days. Working together, in how many days will they complete the work?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e 84/13
Let's assume that the total work to be done is 1 unit.
S can do the work in 14 days, so the fraction of work done by S in one day is:
1/14
T can do the work in 21 days, so the fraction of work done by T in one day is:
1/21
U can do the work in 28 days, so the fraction of work done by U in one day is:
1/28
When working together, the combined fraction of work done by all three in one day is:
1/14 + 1/21 + 1/28
To add these fractions, we need to find the least common multiple of the denominators, which is 84. So, we can write:
1/14 + 1/21 + 1/28 = (6/84) + (4/84) + (3/84) = 13/84
Therefore, when working together, they can complete 13/84th of the work in one day.
To find out how many days it would take to complete the entire work, we can use the formula:
Number of days = Total work / Work done in one day
Total work is 1 unit, and the work done in one day is 13/84 units, so:
Number of days = 1 / (13/84) = 84/13