Question : William can finish a work in 15 days. Joseph can finish the same work in 20 days while Thomas can finish the work in 25 days. How long will it take to finish it if they work together?
Correct Answer 6 18/47 days or 6.383 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by William = 15 days
And, the number of days required to finish the same work by Joseph = 20 days
And, the number of days required to finish the same work by Thomas = 25 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 15 days the work is done by William = 1
∴ The work done by William in 1 day = 1/15
Similarly,
∵ In 20 days the work is done by Joseph = 1
∴ The work done by Joseph in 1 day = 1/20
Similarly,
∵ In 25 days the work is done by Thomas = 1
∴ The work done by Thomas in 1 day = 1/25 part
Now, the work done by William, Joseph, and Thomas together in 1 day
= William's 1 day work + Joseph's 1 day work + Thomas's 1 day work
= 1/15 + 1/20 + 1/25
= 20 + 15 + 12/300
= 47/300 part of work
This means in 1 day, 47/300 part of work is done by William, Joseph and Thomas working together.
Now, the number of days required to finish 47/300 part of work by William, Joseph, and Thomas working together = 1
∴ the number of days required to finish the whole work (1 work) by William + Joseph + Thomas together
= 1/47/300
= 1 × 300/47 = 300/47 days
= 6 18/47 days = or 6.383 days
Thus, William, Joseph, and Thomas working together will finish the total work (1 work) in 6 18/47 days = or 6.383 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 = 15 days
And the number of days required to finish the same work by Joseph = 20 days
And the number of days required to finish the work by Thomas = 25 days
Thus, the number of days required to finish the work by William, Joseph, and Thomas together = ?
Here a = 15 days
And, b = 20 days
And, c = 25 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when William, Joseph, and Thomas working together
= 15 × 20 × 25/15 × 20 + 15 × 25 + 20 × 25 days
= 7500/300 + 375 + 500 days
= 7500/1175 days
= 7500/1175 days
= 7500 ÷ 25/1175 ÷ 25 = 300/47 days
= 6 18/47 days or 6.383
Thus, William, Joseph, and Thomas together will finish the work in 6 18/47 days or 6.383 days Answer
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