Question:
If Brenda can finish the work in 76 days and Arthur can finish the same work in 81 days, then in how many days both can finish the work together?
Correct Answer
39 33/157 days or 39.21 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Brenda = 76 days
And, the number of days to finish the same work by Arthur = 81 days
Thus, the number of days to finish the work by Brenda and Arthur together = ?
Here,
∵ In 76 days the work done by Brenda = 1
∴ In 1 day, the work done by Brenda = 1/76 part
Similarly,
∵ In 81 days the work done by Arthur = 1
∴ In 1 day, the work done by Arthur = 1/81 part
Now, in 1 day, the work done by Brenda and Arthur together
= In 1 day work done by Brenda + In 1 day the work done by Arthur
= 1/76 + 1/81
= 81 + 76/6156
= 157/6156 part of work
This means in 1 day, 157/6156 part of work is done by Brenda and Arthur working together.
Now, the number of days required to finish 157/6156 part of work by Brenda + Arthur working together = 1
∴ the number of days required to finish 1 work by Brenda + Arthur together
= 1/157/6156
= 1 × 6156/157 = 6156/157 days
= 39 33/157 days = or 39.21 days
Thus, Brenda and Arthur working together will finish the work in 39 33/157 days = or 39.21 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 Brenda = 76 days
And the number of days required to finish the same work by Arthur = 81 days
Thus, the number of days required to finish the work Brenda and Arthur working together = ?
Here a = 76 days
And, b = 81 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Brenda and Arthur working together
= 76 × 81/76 + 81 days
= 6156/157 days
= 39 33/157 days or 39.21
Thus, Brenda and Arthur together will finish the work in 39 33/157 days or 39.21 days Answer
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