Question:
If David can finish the work in 10 days and Christopher can finish the same work in 14 days, then in how many days both can finish the work together?
Correct Answer
5 5/6 days or 5.833 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by David = 10 days
And, the number of days to finish the same work by Christopher = 14 days
Thus, the number of days to finish the work by David and Christopher together = ?
Here,
∵ In 10 days the work done by David = 1
∴ In 1 day, the work done by David = 1/10 part
Similarly,
∵ In 14 days the work done by Christopher = 1
∴ In 1 day, the work done by Christopher = 1/14 part
Now, in 1 day, the work done by David and Christopher together
= In 1 day work done by David + In 1 day the work done by Christopher
= 1/10 + 1/14
= 7 + 5/70
= 12/70 part of work
= 12 ÷ 2/70 ÷ 2 part of work
= 6/35 part of work
This means, in 1 day, 6/35 part of the work is done by David and Christopher together.
Now, the number of days required to finish 6/35 part of work by David + Christopher working together = 1
∴ the number of days required to finish 1 work by David + Christopher together
= 1/6/35
= 1 × 35/6 = 35/6 days
= 5 5/6 days = or 5.833 days
Thus, David and Christopher working together will finish the work in 5 5/6 days = or 5.833 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 David = 10 days
And the number of days required to finish the same work by Christopher = 14 days
Thus, the number of days required to finish the work David and Christopher working together = ?
Here a = 10 days
And, b = 14 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when David and Christopher working together
= 10 × 14/10 + 14 days
= 140/24 days
= 140 ÷ 4/24 ÷ 4 = 35/6 days
= 5 5/6 days or 5.833
Thus, David and Christopher together will finish the work in 5 5/6 days or 5.833 days Answer
Similar Questions
(1) Linda can finish a work in 12 days. Barbara can finish the same work in 17 days while Susan can finish the work in 22 days. How long will it take to finish it if they work together?
(2) Jonathan can finish a work in 73 days. Larry can finish the same work in 78 days while Justin can finish the work in 83 days. How long will it take to finish it if they work together?
(3) If Sandra can finish the work in 31 days and Gary can finish the same work in 34 days, then in how many days both can finish the work together?
(4) Jack can finish a work in 99 days. Jerry can finish the same work in 104 days while Tyler can finish the work in 109 days. How long will it take to finish it if they work together?
(5) If Joseph can finish the work in 16 days and Steven can finish the same work in 19 days, then in how many days both can finish the work together?
(6) If Jessica can finish the work in 20 days and Paul can finish the same work in 25 days, then in how many days both can finish the work together?
(7) If Steven can finish the work in 37 days and Jonathan can finish the same work in 42 days, then in how many days both can finish the work together?
(8) Raymond can finish a work in 97 days. Dennis can finish the same work in 102 days while Jerry can finish the work in 107 days. How long will it take to finish it if they work together?
(9) Patricia can finish a work in 8 days. Linda can finish the same work in 13 days while Elizabeth can finish the work in 18 days. How long will it take to finish it if they work together?
(10) Carol can finish a work in 42 days. Amanda can finish the same work in 43 days while Dorothy can finish the work in 44 days. How long will it take to finish it if they work together?