Question:
If James can finish the work in 2 days and John can finish the same work in 5 days, then in how many days both can finish the work together?
Correct Answer
1 3/7 days or 1.429 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by James = 2 days
And, the number of days to finish the same work by John = 5 days
Thus, the number of days to finish the work by James and John together = ?
Here,
∵ In 2 days the work done by James = 1
∴ In 1 day, the work done by James = 1/2 part
Similarly,
∵ In 5 days the work done by John = 1
∴ In 1 day, the work done by John = 1/5 part
Now, in 1 day, the work done by James and John together
= In 1 day work done by James + In 1 day the work done by John
= 1/2 + 1/5
= 5 + 2/10
= 7/10 part of work
This means in 1 day, 7/10 part of work is done by James and John working together.
Now, the number of days required to finish 7/10 part of work by James + John working together = 1
∴ the number of days required to finish 1 work by James + John together
= 1/7/10
= 1 × 10/7 = 10/7 days
= 1 3/7 days = or 1.429 days
Thus, James and John working together will finish the work in 1 3/7 days = or 1.429 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 James = 2 days
And the number of days required to finish the same work by John = 5 days
Thus, the number of days required to finish the work James and John working together = ?
Here a = 2 days
And, b = 5 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when James and John working together
= 2 × 5/2 + 5 days
= 10/7 days
= 1 3/7 days or 1.429
Thus, James and John together will finish the work in 1 3/7 days or 1.429 days Answer
Similar Questions
(1) If George can finish the work in 51 days and Dennis can finish the same work in 56 days, then in how many days both can finish the work together?
(2) If John can finish the work in 6 days and Richard can finish the same work in 10 days, then in how many days both can finish the work together?
(3) 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?
(4) Benjamin can finish a work in 85 days. Gregory can finish the same work in 90 days while Alexander can finish the work in 95 days. How long will it take to finish it if they work together?
(5) Sharon can finish a work in 60 days. Cynthia can finish the same work in 65 days while Kathleen can finish the work in 70 days. How long will it take to finish it if they work together?
(6) If Carol can finish the work in 46 days and Alexander can finish the same work in 51 days, then in how many days both can finish the work together?
(7) Donna can finish a work in 42 days. Carol can finish the same work in 47 days while Amanda can finish the work in 52 days. How long will it take to finish it if they work together?
(8) Charles can finish a work in 19 days. Christopher can finish the same work in 20 days while Daniel can finish the work in 21 days. How long will it take to finish it if they work together?
(9) If Christopher can finish the work in 22 days and Brian can finish the same work in 26 days, then in how many days both can finish the work together?
(10) If Karen can finish the work in 21 days and Kevin can finish the same work in 24 days, then in how many days both can finish the work together?