Question:
If John can finish the work in 9 days and Richard can finish the same work in 14 days, then in how many days both can finish the work together?
Correct Answer
5 11/23 days or 5.478 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by John = 9 days
And, the number of days to finish the same work by Richard = 14 days
Thus, the number of days to finish the work by John and Richard together = ?
Here,
∵ In 9 days the work done by John = 1
∴ In 1 day, the work done by John = 1/9 part
Similarly,
∵ In 14 days the work done by Richard = 1
∴ In 1 day, the work done by Richard = 1/14 part
Now, in 1 day, the work done by John and Richard together
= In 1 day work done by John + In 1 day the work done by Richard
= 1/9 + 1/14
= 14 + 9/126
= 23/126 part of work
This means in 1 day, 23/126 part of work is done by John and Richard working together.
Now, the number of days required to finish 23/126 part of work by John + Richard working together = 1
∴ the number of days required to finish 1 work by John + Richard together
= 1/23/126
= 1 × 126/23 = 126/23 days
= 5 11/23 days = or 5.478 days
Thus, John and Richard working together will finish the work in 5 11/23 days = or 5.478 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 John = 9 days
And the number of days required to finish the same work by Richard = 14 days
Thus, the number of days required to finish the work John and Richard working together = ?
Here a = 9 days
And, b = 14 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when John and Richard working together
= 9 × 14/9 + 14 days
= 126/23 days
= 5 11/23 days or 5.478
Thus, John and Richard together will finish the work in 5 11/23 days or 5.478 days Answer
Similar Questions
(1) If Justin can finish the work in 79 days and Jesse can finish the same work in 84 days, then in how many days both can finish the work together?
(2) 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?
(3) 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?
(4) If Debra can finish the work in 92 days and Elijah can finish the same work in 97 days, then in how many days both can finish the work together?
(5) If Betty can finish the work in 30 days and Jason can finish the same work in 35 days, then in how many days both can finish the work together?
(6) Jessica can finish a work in 16 days. Sarah can finish the same work in 17 days while Karen can finish the work in 18 days. How long will it take to finish it if they work together?
(7) If Raymond can finish the work in 97 days and Eugene can finish the same work in 102 days, then in how many days both can finish the work together?
(8) Rachel can finish a work in 94 days. Janet can finish the same work in 99 days while Catherine can finish the work in 104 days. How long will it take to finish it if they work together?
(9) 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?
(10) If Rebecca can finish the work in 58 days and Henry can finish the same work in 63 days, then in how many days both can finish the work together?