Question:
If George can finish the work in 51 days and Dennis can finish the same work in 56 days, then in how many days both can finish the work together?
Correct Answer
26 74/107 days or 26.692 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by George = 51 days
And, the number of days to finish the same work by Dennis = 56 days
Thus, the number of days to finish the work by George and Dennis together = ?
Here,
∵ In 51 days the work done by George = 1
∴ In 1 day, the work done by George = 1/51 part
Similarly,
∵ In 56 days the work done by Dennis = 1
∴ In 1 day, the work done by Dennis = 1/56 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
= 1/51 + 1/56
= 56 + 51/2856
= 107/2856 part of work
This means in 1 day, 107/2856 part of work is done by George and Dennis working together.
Now, the number of days required to finish 107/2856 part of work by George + Dennis working together = 1
∴ the number of days required to finish 1 work by George + Dennis together
= 1/107/2856
= 1 × 2856/107 = 2856/107 days
= 26 74/107 days = or 26.692 days
Thus, George and Dennis working together will finish the work in 26 74/107 days = or 26.692 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 = 51 days
And the number of days required to finish the same work by Dennis = 56 days
Thus, the number of days required to finish the work George and Dennis working together = ?
Here a = 51 days
And, b = 56 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when George and Dennis working together
= 51 × 56/51 + 56 days
= 2856/107 days
= 26 74/107 days or 26.692
Thus, George and Dennis together will finish the work in 26 74/107 days or 26.692 days Answer
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