Question : If Jacob can finish the work in 65 days and Noah can finish the same work in 70 days, then in how many days both can finish the work together?
Correct Answer 33 19/27 days or 33.704 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Jacob = 65 days
And, the number of days to finish the same work by Noah = 70 days
Thus, the number of days to finish the work by Jacob and Noah together = ?
Here,
∵ In 65 days the work done by Jacob = 1
∴ In 1 day, the work done by Jacob = 1/65 part
Similarly,
∵ In 70 days the work done by Noah = 1
∴ In 1 day, the work done by Noah = 1/70 part
Now, in 1 day, the work done by Jacob and Noah together
= In 1 day work done by Jacob + In 1 day the work done by Noah
= 1/65 + 1/70
= 14 + 13/910
= 27/910 part of work
This means in 1 day, 27/910 part of work is done by Jacob and Noah working together.
Now, the number of days required to finish 27/910 part of work by Jacob + Noah working together = 1
∴ the number of days required to finish 1 work by Jacob + Noah together
= 1/27/910
= 1 × 910/27 = 910/27 days
= 33 19/27 days = or 33.704 days
Thus, Jacob and Noah working together will finish the work in 33 19/27 days = or 33.704 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 Jacob = 65 days
And the number of days required to finish the same work by Noah = 70 days
Thus, the number of days required to finish the work Jacob and Noah working together = ?
Here a = 65 days
And, b = 70 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Jacob and Noah working together
= 65 × 70/65 + 70 days
= 4550/135 days
= 4550 ÷ 5/135 ÷ 5 = 910/27 days
= 33 19/27 days or 33.704
Thus, Jacob and Noah together will finish the work in 33 19/27 days or 33.704 days Answer
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