Question:
David can finish a work in 9 days. William can finish the same work in 10 days while Richard can finish the work in 11 days. How long will it take to finish it if they work together?
Correct Answer
3 93/299 days or 3.311 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by David = 9 days
And, the number of days required to finish the same work by William = 10 days
And, the number of days required to finish the same work by Richard = 11 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 9 days the work is done by David = 1
∴ The work done by David in 1 day = 1/9
Similarly,
∵ In 10 days the work is done by William = 1
∴ The work done by William in 1 day = 1/10
Similarly,
∵ In 11 days the work is done by Richard = 1
∴ The work done by Richard in 1 day = 1/11 part
Now, the work done by David, William, and Richard together in 1 day
= David's 1 day work + William's 1 day work + Richard's 1 day work
= 1/9 + 1/10 + 1/11
= 110 + 99 + 90/990
= 299/990 part of work
This means in 1 day, 299/990 part of work is done by David, William and Richard working together.
Now, the number of days required to finish 299/990 part of work by David, William, and Richard working together = 1
∴ the number of days required to finish the whole work (1 work) by David + William + Richard together
= 1/299/990
= 1 × 990/299 = 990/299 days
= 3 93/299 days = or 3.311 days
Thus, David, William, and Richard working together will finish the total work (1 work) in 3 93/299 days = or 3.311 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 David = 9 days
And the number of days required to finish the same work by William = 10 days
And the number of days required to finish the work by Richard = 11 days
Thus, the number of days required to finish the work by David, William, and Richard together = ?
Here a = 9 days
And, b = 10 days
And, c = 11 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when David, William, and Richard working together
= 9 × 10 × 11/9 × 10 + 9 × 11 + 10 × 11 days
= 990/90 + 99 + 110 days
= 990/299 days
= 990/299 days
= 3 93/299 days or 3.311
Thus, David, William, and Richard together will finish the work in 3 93/299 days or 3.311 days Answer
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