Question:
If Betty can finish the work in 27 days and Jason can finish the same work in 30 days, then in how many days both can finish the work together?
Correct Answer
14 4/19 days or 14.211 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Betty = 27 days
And, the number of days to finish the same work by Jason = 30 days
Thus, the number of days to finish the work by Betty and Jason together = ?
Here,
∵ In 27 days the work done by Betty = 1
∴ In 1 day, the work done by Betty = 1/27 part
Similarly,
∵ In 30 days the work done by Jason = 1
∴ In 1 day, the work done by Jason = 1/30 part
Now, in 1 day, the work done by Betty and Jason together
= In 1 day work done by Betty + In 1 day the work done by Jason
= 1/27 + 1/30
= 10 + 9/270
= 19/270 part of work
This means in 1 day, 19/270 part of work is done by Betty and Jason working together.
Now, the number of days required to finish 19/270 part of work by Betty + Jason working together = 1
∴ the number of days required to finish 1 work by Betty + Jason together
= 1/19/270
= 1 × 270/19 = 270/19 days
= 14 4/19 days = or 14.211 days
Thus, Betty and Jason working together will finish the work in 14 4/19 days = or 14.211 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 Betty = 27 days
And the number of days required to finish the same work by Jason = 30 days
Thus, the number of days required to finish the work Betty and Jason working together = ?
Here a = 27 days
And, b = 30 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Betty and Jason working together
= 27 × 30/27 + 30 days
= 810/57 days
= 810 ÷ 3/57 ÷ 3 = 270/19 days
= 14 4/19 days or 14.211
Thus, Betty and Jason together will finish the work in 14 4/19 days or 14.211 days Answer
Similar Questions
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