Question : If Lisa can finish the work in 26 days and George can finish the same work in 31 days, then in how many days both can finish the work together?
Correct Answer 14 8/57 days or 14.14 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Lisa = 26 days
And, the number of days to finish the same work by George = 31 days
Thus, the number of days to finish the work by Lisa and George together = ?
Here,
∵ In 26 days the work done by Lisa = 1
∴ In 1 day, the work done by Lisa = 1/26 part
Similarly,
∵ In 31 days the work done by George = 1
∴ In 1 day, the work done by George = 1/31 part
Now, in 1 day, the work done by Lisa and George together
= In 1 day work done by Lisa + In 1 day the work done by George
= 1/26 + 1/31
= 31 + 26/806
= 57/806 part of work
This means in 1 day, 57/806 part of work is done by Lisa and George working together.
Now, the number of days required to finish 57/806 part of work by Lisa + George working together = 1
∴ the number of days required to finish 1 work by Lisa + George together
= 1/57/806
= 1 × 806/57 = 806/57 days
= 14 8/57 days = or 14.14 days
Thus, Lisa and George working together will finish the work in 14 8/57 days = or 14.14 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 Lisa = 26 days
And the number of days required to finish the same work by George = 31 days
Thus, the number of days required to finish the work Lisa and George working together = ?
Here a = 26 days
And, b = 31 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Lisa and George working together
= 26 × 31/26 + 31 days
= 806/57 days
= 14 8/57 days or 14.14
Thus, Lisa and George together will finish the work in 14 8/57 days or 14.14 days Answer
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