Question:
If George can finish the work in 48 days and Dennis can finish the same work in 52 days, then in how many days both can finish the work together?
Correct Answer
24 24/25 days or 24.96 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by George = 48 days
And, the number of days to finish the same work by Dennis = 52 days
Thus, the number of days to finish the work by George and Dennis together = ?
Here,
∵ In 48 days the work done by George = 1
∴ In 1 day, the work done by George = 1/48 part
Similarly,
∵ In 52 days the work done by Dennis = 1
∴ In 1 day, the work done by Dennis = 1/52 part
Now, in 1 day, the work done by George and Dennis together
= In 1 day work done by George + In 1 day the work done by Dennis
= 1/48 + 1/52
= 13 + 12/624
= 25/624 part of work
This means in 1 day, 25/624 part of work is done by George and Dennis working together.
Now, the number of days required to finish 25/624 part of work by George + Dennis working together = 1
∴ the number of days required to finish 1 work by George + Dennis together
= 1/25/624
= 1 × 624/25 = 624/25 days
= 24 24/25 days = or 24.96 days
Thus, George and Dennis working together will finish the work in 24 24/25 days = or 24.96 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 George = 48 days
And the number of days required to finish the same work by Dennis = 52 days
Thus, the number of days required to finish the work George and Dennis working together = ?
Here a = 48 days
And, b = 52 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when George and Dennis working together
= 48 × 52/48 + 52 days
= 2496/100 days
= 2496 ÷ 4/100 ÷ 4 = 624/25 days
= 24 24/25 days or 24.96
Thus, George and Dennis together will finish the work in 24 24/25 days or 24.96 days Answer
Similar Questions
(1) If Robert can finish a work in 5 days and Bob can finish the same work in 6 days, then in how many days they both can finish the work working together?
(2) If Mary can finish the work in 25 days and Michael can finish the same work in 41 days, then in how many days both can finish the work together?
(3) Kevin can finish a work in 47 days. George can finish the same work in 52 days while Timothy can finish the work in 57 days. How long will it take to finish it if they work together?
(4) If Kevin can finish the work in 44 days and Frank can finish the same work in 48 days, then in how many days both can finish the work together?
(5) If Donald can finish the work in 32 days and Nicholas can finish the same work in 35 days, then in how many days both can finish the work together?
(6) Emma can finish a work in 80 days. Helen can finish the same work in 85 days while Samantha can finish the work in 90 days. How long will it take to finish it if they work together?
(7) If Nicholas can finish the work in 69 days and Roger can finish the same work in 74 days, then in how many days both can finish the work together?
(8) 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?
(9) If Sandra can finish the work in 34 days and Gary can finish the same work in 39 days, then in how many days both can finish the work together?
(10) Ronald can finish a work in 55 days. Jason can finish the same work in 60 days while Jeffrey can finish the work in 65 days. How long will it take to finish it if they work together?