Question:
If Charles can finish the work in 20 days and Kenneth can finish the same work in 24 days, then in how many days both can finish the work together?
Correct Answer
10 10/11 days or 10.909 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Charles = 20 days
And, the number of days to finish the same work by Kenneth = 24 days
Thus, the number of days to finish the work by Charles and Kenneth together = ?
Here,
∵ In 20 days the work done by Charles = 1
∴ In 1 day, the work done by Charles = 1/20 part
Similarly,
∵ In 24 days the work done by Kenneth = 1
∴ In 1 day, the work done by Kenneth = 1/24 part
Now, in 1 day, the work done by Charles and Kenneth together
= In 1 day work done by Charles + In 1 day the work done by Kenneth
= 1/20 + 1/24
= 6 + 5/120
= 11/120 part of work
This means in 1 day, 11/120 part of work is done by Charles and Kenneth working together.
Now, the number of days required to finish 11/120 part of work by Charles + Kenneth working together = 1
∴ the number of days required to finish 1 work by Charles + Kenneth together
= 1/11/120
= 1 × 120/11 = 120/11 days
= 10 10/11 days = or 10.909 days
Thus, Charles and Kenneth working together will finish the work in 10 10/11 days = or 10.909 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 Charles = 20 days
And the number of days required to finish the same work by Kenneth = 24 days
Thus, the number of days required to finish the work Charles and Kenneth working together = ?
Here a = 20 days
And, b = 24 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Charles and Kenneth working together
= 20 × 24/20 + 24 days
= 480/44 days
= 480 ÷ 4/44 ÷ 4 = 120/11 days
= 10 10/11 days or 10.909
Thus, Charles and Kenneth together will finish the work in 10 10/11 days or 10.909 days Answer
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