Question:
Donald can finish a work in 31 days. Steven can finish the same work in 32 days while Paul can finish the work in 33 days. How long will it take to finish it if they work together?
Correct Answer
10 2026/3071 days or 10.66 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Donald = 31 days
And, the number of days required to finish the same work by Steven = 32 days
And, the number of days required to finish the same work by Paul = 33 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 31 days the work is done by Donald = 1
∴ The work done by Donald in 1 day = 1/31
Similarly,
∵ In 32 days the work is done by Steven = 1
∴ The work done by Steven in 1 day = 1/32
Similarly,
∵ In 33 days the work is done by Paul = 1
∴ The work done by Paul in 1 day = 1/33 part
Now, the work done by Donald, Steven, and Paul together in 1 day
= Donald's 1 day work + Steven's 1 day work + Paul's 1 day work
= 1/31 + 1/32 + 1/33
= 1056 + 1023 + 992/32736
= 3071/32736 part of work
This means in 1 day, 3071/32736 part of work is done by Donald, Steven and Paul working together.
Now, the number of days required to finish 3071/32736 part of work by Donald, Steven, and Paul working together = 1
∴ the number of days required to finish the whole work (1 work) by Donald + Steven + Paul together
= 1/3071/32736
= 1 × 32736/3071 = 32736/3071 days
= 10 2026/3071 days = or 10.66 days
Thus, Donald, Steven, and Paul working together will finish the total work (1 work) in 10 2026/3071 days = or 10.66 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 Donald = 31 days
And the number of days required to finish the same work by Steven = 32 days
And the number of days required to finish the work by Paul = 33 days
Thus, the number of days required to finish the work by Donald, Steven, and Paul together = ?
Here a = 31 days
And, b = 32 days
And, c = 33 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Donald, Steven, and Paul working together
= 31 × 32 × 33/31 × 32 + 31 × 33 + 32 × 33 days
= 32736/992 + 1023 + 1056 days
= 32736/3071 days
= 32736/3071 days
= 10 2026/3071 days or 10.66
Thus, Donald, Steven, and Paul together will finish the work in 10 2026/3071 days or 10.66 days Answer
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