Question:
If Jason can finish the work in 59 days and Douglas can finish the same work in 64 days, then in how many days both can finish the work together?
Correct Answer
30 86/123 days or 30.699 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Jason = 59 days
And, the number of days to finish the same work by Douglas = 64 days
Thus, the number of days to finish the work by Jason and Douglas together = ?
Here,
∵ In 59 days the work done by Jason = 1
∴ In 1 day, the work done by Jason = 1/59 part
Similarly,
∵ In 64 days the work done by Douglas = 1
∴ In 1 day, the work done by Douglas = 1/64 part
Now, in 1 day, the work done by Jason and Douglas together
= In 1 day work done by Jason + In 1 day the work done by Douglas
= 1/59 + 1/64
= 64 + 59/3776
= 123/3776 part of work
This means in 1 day, 123/3776 part of work is done by Jason and Douglas working together.
Now, the number of days required to finish 123/3776 part of work by Jason + Douglas working together = 1
∴ the number of days required to finish 1 work by Jason + Douglas together
= 1/123/3776
= 1 × 3776/123 = 3776/123 days
= 30 86/123 days = or 30.699 days
Thus, Jason and Douglas working together will finish the work in 30 86/123 days = or 30.699 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 Jason = 59 days
And the number of days required to finish the same work by Douglas = 64 days
Thus, the number of days required to finish the work Jason and Douglas working together = ?
Here a = 59 days
And, b = 64 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Jason and Douglas working together
= 59 × 64/59 + 64 days
= 3776/123 days
= 30 86/123 days or 30.699
Thus, Jason and Douglas together will finish the work in 30 86/123 days or 30.699 days Answer
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