Question:
If James can finish the work in 24 days and John can finish the same work in 40 days, then in how many days both can finish the work together?
Correct Answer
15 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by James = 24 days
And, the number of days to finish the same work by John = 40 days
Thus, the number of days to finish the work by James and John together = ?
Here,
∵ In 24 days the work done by James = 1
∴ In 1 day, the work done by James = 1/24 part
Similarly,
∵ In 40 days the work done by John = 1
∴ In 1 day, the work done by John = 1/40 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
= 1/24 + 1/40
= 5 + 3/120
= 8/120 part of work
= 8 ÷ 8/120 ÷ 8 part of work
= 1/15 part of work
This means, in 1 day, 1/15 part of the work is done by James and John together.
Now, the number of days required to finish 1/15 part of work by James + John working together = 1
∴ the number of days required to finish 1 work by James + John together
= 1/1/15
= 1 × 15/1 = 15/1 days
= 15 days
Thus, James and John working together will finish the work in 15 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 = 24 days
And the number of days required to finish the same work by John = 40 days
Thus, the number of days required to finish the work James and John working together = ?
Here a = 24 days
And, b = 40 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when James and John working together
= 24 × 40/24 + 40 days
= 960/64 days
= 960 ÷ 64/64 ÷ 64 = 15/1 days
= 15 days
Thus, James and John together will finish the work in 15 days Answer
Similar Questions
(1) Christopher can finish a work in 21 days. Daniel can finish the same work in 22 days while Matthew can finish the work in 23 days. How long will it take to finish it if they work together?
(2) James can finish a work in 5 days. John can finish the same work in 10 days while Michael can finish the work in 15 days. How long will it take to finish it if they work together?
(3) If Margaret can finish the work in 29 days and Ryan can finish the same work in 33 days, then in how many days both can finish the work together?
(4) 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?
(5) If Patricia can finish the work in 27 days and William can finish the same work in 43 days, then in how many days both can finish the work together?
(6) If Charles can finish the work in 23 days and Kenneth can finish the same work in 28 days, then in how many days both can finish the work together?
(7) If Robert can finish the work in 4 days and David can finish the same work in 8 days, then in how many days both can finish the work together?
(8) If Melissa can finish the work in 52 days and Jerry can finish the same work in 57 days, then in how many days both can finish the work together?
(9) Donald can finish a work in 31 days. Steven can finish the same work in 32 days while Paul can finish the work in 33 days. How long will it take to finish it if they work together?
(10) Steven can finish a work in 37 days. Andrew can finish the same work in 42 days while Joshua can finish the work in 47 days. How long will it take to finish it if they work together?