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 & 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