Question : Michael can finish a work in 11 days. William can finish the same work in 16 days while Richard can finish the work in 21 days. How long will it take to finish it if they work together?
Correct Answer 4 724/743 days or 4.974 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Michael = 11 days
And, the number of days required to finish the same work by William = 16 days
And, the number of days required to finish the same work by Richard = 21 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 11 days the work is done by Michael = 1
∴ The work done by Michael in 1 day = 1/11
Similarly,
∵ In 16 days the work is done by William = 1
∴ The work done by William in 1 day = 1/16
Similarly,
∵ In 21 days the work is done by Richard = 1
∴ The work done by Richard in 1 day = 1/21 part
Now, the work done by Michael, William, and Richard together in 1 day
= Michael's 1 day work + William's 1 day work + Richard's 1 day work
= 1/11 + 1/16 + 1/21
= 336 + 231 + 176/3696
= 743/3696 part of work
This means in 1 day, 743/3696 part of work is done by Michael, William and Richard working together.
Now, the number of days required to finish 743/3696 part of work by Michael, William, and Richard working together = 1
∴ the number of days required to finish the whole work (1 work) by Michael + William + Richard together
= 1/743/3696
= 1 × 3696/743 = 3696/743 days
= 4 724/743 days = or 4.974 days
Thus, Michael, William, and Richard working together will finish the total work (1 work) in 4 724/743 days = or 4.974 days Answer
Shortcut Trick to solve the problems based on time and work using formula
Case: If A can finish a work in a days, B can finish the same work in b days, and C can finish the work in c days
then working together the number of days required to finish the work
= a × b × c/ab + ac + bc days.
Here given,
The number of days required to finish the work by Michael = 11 days
And the number of days required to finish the same work by William = 16 days
And the number of days required to finish the work by Richard = 21 days
Thus, the number of days required to finish the work by Michael, William, and Richard together = ?
Here a = 11 days
And, b = 16 days
And, c = 21 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Michael, William, and Richard working together
= 11 × 16 × 21/11 × 16 + 11 × 21 + 16 × 21 days
= 3696/176 + 231 + 336 days
= 3696/743 days
= 3696/743 days
= 4 724/743 days or 4.974
Thus, Michael, William, and Richard together will finish the work in 4 724/743 days or 4.974 days Answer
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