Question:
If Pamela can finish the work in 78 days and Dylan can finish the same work in 83 days, then in how many days both can finish the work together?
Correct Answer
40 34/161 days or 40.211 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Pamela = 78 days
And, the number of days to finish the same work by Dylan = 83 days
Thus, the number of days to finish the work by Pamela and Dylan together = ?
Here,
∵ In 78 days the work done by Pamela = 1
∴ In 1 day, the work done by Pamela = 1/78 part
Similarly,
∵ In 83 days the work done by Dylan = 1
∴ In 1 day, the work done by Dylan = 1/83 part
Now, in 1 day, the work done by Pamela and Dylan together
= In 1 day work done by Pamela + In 1 day the work done by Dylan
= 1/78 + 1/83
= 83 + 78/6474
= 161/6474 part of work
This means in 1 day, 161/6474 part of work is done by Pamela and Dylan working together.
Now, the number of days required to finish 161/6474 part of work by Pamela + Dylan working together = 1
∴ the number of days required to finish 1 work by Pamela + Dylan together
= 1/161/6474
= 1 × 6474/161 = 6474/161 days
= 40 34/161 days = or 40.211 days
Thus, Pamela and Dylan working together will finish the work in 40 34/161 days = or 40.211 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, and B can finish the same work in b days,
then working together the number of days require to finish the work
= a × b/a + b days.
Here given,
The number of days required to finish the work by Pamela = 78 days
And the number of days required to finish the same work by Dylan = 83 days
Thus, the number of days required to finish the work Pamela and Dylan working together = ?
Here a = 78 days
And, b = 83 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Pamela and Dylan working together
= 78 × 83/78 + 83 days
= 6474/161 days
= 40 34/161 days or 40.211
Thus, Pamela and Dylan together will finish the work in 40 34/161 days or 40.211 days Answer
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