Question : David can finish a work in 13 days. Richard can finish the same work in 18 days while Joseph can finish the work in 23 days. How long will it take to finish it if they work together?
Correct Answer 5 647/947 days or 5.683 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by David = 13 days
And, the number of days required to finish the same work by Richard = 18 days
And, the number of days required to finish the same work by Joseph = 23 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 13 days the work is done by David = 1
∴ The work done by David in 1 day = 1/13
Similarly,
∵ In 18 days the work is done by Richard = 1
∴ The work done by Richard in 1 day = 1/18
Similarly,
∵ In 23 days the work is done by Joseph = 1
∴ The work done by Joseph in 1 day = 1/23 part
Now, the work done by David, Richard, and Joseph together in 1 day
= David's 1 day work + Richard's 1 day work + Joseph's 1 day work
= 1/13 + 1/18 + 1/23
= 414 + 299 + 234/5382
= 947/5382 part of work
This means in 1 day, 947/5382 part of work is done by David, Richard and Joseph working together.
Now, the number of days required to finish 947/5382 part of work by David, Richard, and Joseph working together = 1
∴ the number of days required to finish the whole work (1 work) by David + Richard + Joseph together
= 1/947/5382
= 1 × 5382/947 = 5382/947 days
= 5 647/947 days = or 5.683 days
Thus, David, Richard, and Joseph working together will finish the total work (1 work) in 5 647/947 days = or 5.683 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 = 13 days
And the number of days required to finish the same work by Richard = 18 days
And the number of days required to finish the work by Joseph = 23 days
Thus, the number of days required to finish the work by David, Richard, and Joseph together = ?
Here a = 13 days
And, b = 18 days
And, c = 23 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when David, Richard, and Joseph working together
= 13 × 18 × 23/13 × 18 + 13 × 23 + 18 × 23 days
= 5382/234 + 299 + 414 days
= 5382/947 days
= 5382/947 days
= 5 647/947 days or 5.683
Thus, David, Richard, and Joseph together will finish the work in 5 647/947 days or 5.683 days Answer
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