Question : If Deborah can finish the work in 54 days and Aaron can finish the same work in 59 days, then in how many days both can finish the work together?
Correct Answer 28 22/113 days or 28.195 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Deborah = 54 days
And, the number of days to finish the same work by Aaron = 59 days
Thus, the number of days to finish the work by Deborah and Aaron together = ?
Here,
∵ In 54 days the work done by Deborah = 1
∴ In 1 day, the work done by Deborah = 1/54 part
Similarly,
∵ In 59 days the work done by Aaron = 1
∴ In 1 day, the work done by Aaron = 1/59 part
Now, in 1 day, the work done by Deborah and Aaron together
= In 1 day work done by Deborah + In 1 day the work done by Aaron
= 1/54 + 1/59
= 59 + 54/3186
= 113/3186 part of work
This means in 1 day, 113/3186 part of work is done by Deborah and Aaron working together.
Now, the number of days required to finish 113/3186 part of work by Deborah + Aaron working together = 1
∴ the number of days required to finish 1 work by Deborah + Aaron together
= 1/113/3186
= 1 × 3186/113 = 3186/113 days
= 28 22/113 days = or 28.195 days
Thus, Deborah and Aaron working together will finish the work in 28 22/113 days = or 28.195 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 Deborah = 54 days
And the number of days required to finish the same work by Aaron = 59 days
Thus, the number of days required to finish the work Deborah and Aaron working together = ?
Here a = 54 days
And, b = 59 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Deborah and Aaron working together
= 54 × 59/54 + 59 days
= 3186/113 days
= 28 22/113 days or 28.195
Thus, Deborah and Aaron together will finish the work in 28 22/113 days or 28.195 days Answer
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