Question:
If Barbara can finish the work in 16 days and Anthony can finish the same work in 21 days, then in how many days both can finish the work together?
Correct Answer
9 3/37 days or 9.081 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Barbara = 16 days
And, the number of days to finish the same work by Anthony = 21 days
Thus, the number of days to finish the work by Barbara and Anthony together = ?
Here,
∵ In 16 days the work done by Barbara = 1
∴ In 1 day, the work done by Barbara = 1/16 part
Similarly,
∵ In 21 days the work done by Anthony = 1
∴ In 1 day, the work done by Anthony = 1/21 part
Now, in 1 day, the work done by Barbara and Anthony together
= In 1 day work done by Barbara + In 1 day the work done by Anthony
= 1/16 + 1/21
= 21 + 16/336
= 37/336 part of work
This means in 1 day, 37/336 part of work is done by Barbara and Anthony working together.
Now, the number of days required to finish 37/336 part of work by Barbara + Anthony working together = 1
∴ the number of days required to finish 1 work by Barbara + Anthony together
= 1/37/336
= 1 × 336/37 = 336/37 days
= 9 3/37 days = or 9.081 days
Thus, Barbara and Anthony working together will finish the work in 9 3/37 days = or 9.081 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 Barbara = 16 days
And the number of days required to finish the same work by Anthony = 21 days
Thus, the number of days required to finish the work Barbara and Anthony working together = ?
Here a = 16 days
And, b = 21 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Barbara and Anthony working together
= 16 × 21/16 + 21 days
= 336/37 days
= 9 3/37 days or 9.081
Thus, Barbara and Anthony together will finish the work in 9 3/37 days or 9.081 days Answer
Similar Questions
(1) Robert can finish a work in 3 days. John can finish the same work in 4 days while Michael can finish the work in 5 days. How long will it take to finish it if they work together?
(2) Debra can finish a work in 92 days. Carolyn can finish the same work in 97 days while Janet can finish the work in 102 days. How long will it take to finish it if they work together?
(3) George can finish a work in 47 days. Timothy can finish the same work in 48 days while Ronald can finish the work in 49 days. How long will it take to finish it if they work together?
(4) If Matthew can finish the work in 29 days and Edward can finish the same work in 34 days, then in how many days both can finish the work together?
(5) If Susan can finish the work in 15 days and Donald can finish the same work in 19 days, then in how many days both can finish the work together?
(6) If Richard can finish the work in 14 days and Mark can finish the same work in 17 days, then in how many days both can finish the work together?
(7) Gary can finish a work in 67 days. Eric can finish the same work in 72 days while Jonathan can finish the work in 77 days. How long will it take to finish it if they work together?
(8) Dorothy can finish a work in 50 days. Deborah can finish the same work in 55 days while Stephanie can finish the work in 60 days. How long will it take to finish it if they work together?
(9) Karen can finish a work in 20 days. Lisa can finish the same work in 21 days while Nancy can finish the work in 22 days. How long will it take to finish it if they work together?
(10) John can finish a work in 5 days. Michael can finish the same work in 6 days while David can finish the work in 7 days. How long will it take to finish it if they work together?