Question:
Christopher can finish a work in 25 days. Matthew can finish the same work in 30 days while Anthony can finish the work in 35 days. How long will it take to finish it if they work together?
Correct Answer
9 87/107 days or 9.813 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Christopher = 25 days
And, the number of days required to finish the same work by Matthew = 30 days
And, the number of days required to finish the same work by Anthony = 35 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 25 days the work is done by Christopher = 1
∴ The work done by Christopher in 1 day = 1/25
Similarly,
∵ In 30 days the work is done by Matthew = 1
∴ The work done by Matthew in 1 day = 1/30
Similarly,
∵ In 35 days the work is done by Anthony = 1
∴ The work done by Anthony in 1 day = 1/35 part
Now, the work done by Christopher, Matthew, and Anthony together in 1 day
= Christopher's 1 day work + Matthew's 1 day work + Anthony's 1 day work
= 1/25 + 1/30 + 1/35
= 42 + 35 + 30/1050
= 107/1050 part of work
This means in 1 day, 107/1050 part of work is done by Christopher, Matthew and Anthony working together.
Now, the number of days required to finish 107/1050 part of work by Christopher, Matthew, and Anthony working together = 1
∴ the number of days required to finish the whole work (1 work) by Christopher + Matthew + Anthony together
= 1/107/1050
= 1 × 1050/107 = 1050/107 days
= 9 87/107 days = or 9.813 days
Thus, Christopher, Matthew, and Anthony working together will finish the total work (1 work) in 9 87/107 days = or 9.813 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 Christopher = 25 days
And the number of days required to finish the same work by Matthew = 30 days
And the number of days required to finish the work by Anthony = 35 days
Thus, the number of days required to finish the work by Christopher, Matthew, and Anthony together = ?
Here a = 25 days
And, b = 30 days
And, c = 35 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Christopher, Matthew, and Anthony working together
= 25 × 30 × 35/25 × 30 + 25 × 35 + 30 × 35 days
= 26250/750 + 875 + 1050 days
= 26250/2675 days
= 26250/2675 days
= 26250 ÷ 25/2675 ÷ 25 = 1050/107 days
= 9 87/107 days or 9.813
Thus, Christopher, Matthew, and Anthony together will finish the work in 9 87/107 days or 9.813 days Answer
Similar Questions
(1) Samantha can finish a work in 86 days. Christine can finish the same work in 91 days while Debra can finish the work in 96 days. How long will it take to finish it if they work together?
(2) If Carol can finish the work in 43 days and Alexander can finish the same work in 46 days, then in how many days both can finish the work together?
(3) If Rebecca can finish the work in 58 days and Henry can finish the same work in 63 days, then in how many days both can finish the work together?
(4) If Karen can finish the work in 24 days and Kevin can finish the same work in 29 days, then in how many days both can finish the work together?
(5) If Paul can finish the work in 36 days and Larry can finish the same work in 40 days, then in how many days both can finish the work together?
(6) If John can finish the work in 9 days and Richard can finish the same work in 14 days, then in how many days both can finish the work together?
(7) If A can do a piece of work in 2 days, B can do the same piece of work in 3 days, while C alone can do the same work in 4 days. Find the number of days to finish the work when they all will work together.
(8) If James can finish the work in 2 days and John can finish the same work in 5 days, then in how many days both can finish the work together?
(9) If Steven can finish the work in 37 days and Jonathan can finish the same work in 42 days, then in how many days both can finish the work together?
(10) If Linda can finish the work in 9 days and Charles can finish the same work in 13 days, then in how many days both can finish the work together?