Question:
If Rebecca can finish the work in 58 days and Henry can finish the same work in 63 days, then in how many days both can finish the work together?
Correct Answer
30 24/121 days or 30.198 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Rebecca = 58 days
And, the number of days to finish the same work by Henry = 63 days
Thus, the number of days to finish the work by Rebecca and Henry together = ?
Here,
∵ In 58 days the work done by Rebecca = 1
∴ In 1 day, the work done by Rebecca = 1/58 part
Similarly,
∵ In 63 days the work done by Henry = 1
∴ In 1 day, the work done by Henry = 1/63 part
Now, in 1 day, the work done by Rebecca and Henry together
= In 1 day work done by Rebecca + In 1 day the work done by Henry
= 1/58 + 1/63
= 63 + 58/3654
= 121/3654 part of work
This means in 1 day, 121/3654 part of work is done by Rebecca and Henry working together.
Now, the number of days required to finish 121/3654 part of work by Rebecca + Henry working together = 1
∴ the number of days required to finish 1 work by Rebecca + Henry together
= 1/121/3654
= 1 × 3654/121 = 3654/121 days
= 30 24/121 days = or 30.198 days
Thus, Rebecca and Henry working together will finish the work in 30 24/121 days = or 30.198 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 Rebecca = 58 days
And the number of days required to finish the same work by Henry = 63 days
Thus, the number of days required to finish the work Rebecca and Henry working together = ?
Here a = 58 days
And, b = 63 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Rebecca and Henry working together
= 58 × 63/58 + 63 days
= 3654/121 days
= 30 24/121 days or 30.198
Thus, Rebecca and Henry together will finish the work in 30 24/121 days or 30.198 days Answer
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