Question:
If Matthew can finish the work in 26 days and Edward can finish the same work in 30 days, then in how many days both can finish the work together?
Correct Answer
13 13/14 days or 13.929 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Matthew = 26 days
And, the number of days to finish the same work by Edward = 30 days
Thus, the number of days to finish the work by Matthew and Edward together = ?
Here,
∵ In 26 days the work done by Matthew = 1
∴ In 1 day, the work done by Matthew = 1/26 part
Similarly,
∵ In 30 days the work done by Edward = 1
∴ In 1 day, the work done by Edward = 1/30 part
Now, in 1 day, the work done by Matthew and Edward together
= In 1 day work done by Matthew + In 1 day the work done by Edward
= 1/26 + 1/30
= 15 + 13/390
= 28/390 part of work
= 28 ÷ 2/390 ÷ 2 part of work
= 14/195 part of work
This means, in 1 day, 14/195 part of the work is done by Matthew and Edward together.
Now, the number of days required to finish 14/195 part of work by Matthew + Edward working together = 1
∴ the number of days required to finish 1 work by Matthew + Edward together
= 1/14/195
= 1 × 195/14 = 195/14 days
= 13 13/14 days = or 13.929 days
Thus, Matthew and Edward working together will finish the work in 13 13/14 days = or 13.929 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 Matthew = 26 days
And the number of days required to finish the same work by Edward = 30 days
Thus, the number of days required to finish the work Matthew and Edward working together = ?
Here a = 26 days
And, b = 30 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Matthew and Edward working together
= 26 × 30/26 + 30 days
= 780/56 days
= 780 ÷ 4/56 ÷ 4 = 195/14 days
= 13 13/14 days or 13.929
Thus, Matthew and Edward together will finish the work in 13 13/14 days or 13.929 days Answer
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