Question : Raymond can finish a work in 97 days. Dennis can finish the same work in 102 days while Jerry can finish the work in 107 days. How long will it take to finish it if they work together?
Correct Answer 33 29487/31187 days or 33.945 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Raymond = 97 days
And, the number of days required to finish the same work by Dennis = 102 days
And, the number of days required to finish the same work by Jerry = 107 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 97 days the work is done by Raymond = 1
∴ The work done by Raymond in 1 day = 1/97
Similarly,
∵ In 102 days the work is done by Dennis = 1
∴ The work done by Dennis in 1 day = 1/102
Similarly,
∵ In 107 days the work is done by Jerry = 1
∴ The work done by Jerry in 1 day = 1/107 part
Now, the work done by Raymond, Dennis, and Jerry together in 1 day
= Raymond's 1 day work + Dennis's 1 day work + Jerry's 1 day work
= 1/97 + 1/102 + 1/107
= 10914 + 10379 + 9894/1058658
= 31187/1058658 part of work
This means in 1 day, 31187/1058658 part of work is done by Raymond, Dennis and Jerry working together.
Now, the number of days required to finish 31187/1058658 part of work by Raymond, Dennis, and Jerry working together = 1
∴ the number of days required to finish the whole work (1 work) by Raymond + Dennis + Jerry together
= 1/31187/1058658
= 1 × 1058658/31187 = 1058658/31187 days
= 33 29487/31187 days = or 33.945 days
Thus, Raymond, Dennis, and Jerry working together will finish the total work (1 work) in 33 29487/31187 days = or 33.945 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 Raymond = 97 days
And the number of days required to finish the same work by Dennis = 102 days
And the number of days required to finish the work by Jerry = 107 days
Thus, the number of days required to finish the work by Raymond, Dennis, and Jerry together = ?
Here a = 97 days
And, b = 102 days
And, c = 107 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Raymond, Dennis, and Jerry working together
= 97 × 102 × 107/97 × 102 + 97 × 107 + 102 × 107 days
= 1058658/9894 + 10379 + 10914 days
= 1058658/31187 days
= 1058658/31187 days
= 33 29487/31187 days or 33.945
Thus, Raymond, Dennis, and Jerry together will finish the work in 33 29487/31187 days or 33.945 days Answer
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