Question:
If Robert can finish a work in 4 days and Bob can finish the same work in 6 days, then in how many days they both can finish the work working together?
Correct Answer
22/5 days or 2.4 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Robert = 4 days
And, the number of days to finish the same work by Bob = 6 days
Thus, the number of days to finish the work by Rober and Bob working together = ?
Here, ∵ In 4 days the work done by Robert = 1
∴ In 1 day, the work done by Robert = 1/4
Similarly, ∵ In 6 days the work done by Bob = 1
∴ In 1 day, the work done by Bob = 1/6
Now, in 1 day, the work done by Robert and Bob working together
= In 1 day work done by Robert + In 1 day the work done by Bob
= 1/4 + 1/6
= 3 + 2/12
= 5/12
This means in 1 day, 5/12 part of work is done by Robert and Bob working together.
Now, the number of days required to finish 5/12 work by Robert + Bob working together = 1
∴ the number of days required to finish 1 work by Rpbert + Bob working together
= 1/5/12
= 1 × 12/5 days = 2 2/5 days = 2.4 days
Thus, Robert and Bob working together will finish the work in 2 2/5 days or 2.4 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 to finish the work by Robert = 4 days
And, the number of days to finish the same work by Bob = 6 days
Thus, the number of days to finish the work by Robert and Bob working together = ?
Here "a" = 4 days
And, "b" = 6 days
Thus, using formula a × b/a + b days
The number of days reqire to finish the work when Robert and Bob work together
= 4 × 6/4 + 6
= 24 12/10 5
= 12/5 = 2 2/5 days = 2.4 days
Thus, Robert and Bob working together will finish the work in 2 2/5 days or 2.4 days. Answer
Similar Questions
(1) If Betty can finish the work in 27 days and Jason can finish the same work in 30 days, then in how many days both can finish the work together?
(2) If Matthew can finish the work in 26 days and Edward can finish the same work in 29 days, then in how many days both can finish the work together?
(3) Matthew can finish a work in 25 days. Anthony can finish the same work in 26 days while Mark can finish the work in 27 days. How long will it take to finish it if they work together?
(4) If Karen can finish the work in 24 days and Kevin can finish the same work in 29 days, then in how many days both can finish the work together?
(5) If Kimberly can finish the work in 35 days and Stephen can finish the same work in 38 days, then in how many days both can finish the work together?
(6) If Kenneth can finish the work in 42 days and Gregory can finish the same work in 45 days, then in how many days both can finish the work together?
(7) Elizabeth can finish a work in 10 days. Barbara can finish the same work in 11 days while Susan can finish the work in 12 days. How long will it take to finish it if they work together?
(8) If Amy can finish the work in 68 days and Keith can finish the same work in 73 days, then in how many days both can finish the work together?
(9) Mark can finish a work in 29 days. Donald can finish the same work in 30 days while Steven can finish the work in 31 days. How long will it take to finish it if they work together?
(10) If Susan can finish the work in 18 days and Donald can finish the same work in 23 days, then in how many days both can finish the work together?