Question:
William can finish a work in 11 days. Richard can finish the same work in 12 days while Joseph can finish the work in 13 days. How long will it take to finish it if they work together?
Correct Answer
3 423/431 days or 3.981 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by William = 11 days
And, the number of days required to finish the same work by Richard = 12 days
And, the number of days required to finish the same work by Joseph = 13 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 William = 1
∴ The work done by William in 1 day = 1/11
Similarly,
∵ In 12 days the work is done by Richard = 1
∴ The work done by Richard in 1 day = 1/12
Similarly,
∵ In 13 days the work is done by Joseph = 1
∴ The work done by Joseph in 1 day = 1/13 part
Now, the work done by William, Richard, and Joseph together in 1 day
= William's 1 day work + Richard's 1 day work + Joseph's 1 day work
= 1/11 + 1/12 + 1/13
= 156 + 143 + 132/1716
= 431/1716 part of work
This means in 1 day, 431/1716 part of work is done by William, Richard and Joseph working together.
Now, the number of days required to finish 431/1716 part of work by William, Richard, and Joseph working together = 1
∴ the number of days required to finish the whole work (1 work) by William + Richard + Joseph together
= 1/431/1716
= 1 × 1716/431 = 1716/431 days
= 3 423/431 days = or 3.981 days
Thus, William, Richard, and Joseph working together will finish the total work (1 work) in 3 423/431 days = or 3.981 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 William = 11 days
And the number of days required to finish the same work by Richard = 12 days
And the number of days required to finish the work by Joseph = 13 days
Thus, the number of days required to finish the work by William, Richard, and Joseph together = ?
Here a = 11 days
And, b = 12 days
And, c = 13 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when William, Richard, and Joseph working together
= 11 × 12 × 13/11 × 12 + 11 × 13 + 12 × 13 days
= 1716/132 + 143 + 156 days
= 1716/431 days
= 1716/431 days
= 3 423/431 days or 3.981
Thus, William, Richard, and Joseph together will finish the work in 3 423/431 days or 3.981 days Answer
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