Question:
If Anthony can finish the work in 28 days and Jeffrey can finish the same work in 32 days, then in how many days both can finish the work together?
Correct Answer
14 14/15 days or 14.933 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Anthony = 28 days
And, the number of days to finish the same work by Jeffrey = 32 days
Thus, the number of days to finish the work by Anthony and Jeffrey together = ?
Here,
∵ In 28 days the work done by Anthony = 1
∴ In 1 day, the work done by Anthony = 1/28 part
Similarly,
∵ In 32 days the work done by Jeffrey = 1
∴ In 1 day, the work done by Jeffrey = 1/32 part
Now, in 1 day, the work done by Anthony and Jeffrey together
= In 1 day work done by Anthony + In 1 day the work done by Jeffrey
= 1/28 + 1/32
= 8 + 7/224
= 15/224 part of work
This means in 1 day, 15/224 part of work is done by Anthony and Jeffrey working together.
Now, the number of days required to finish 15/224 part of work by Anthony + Jeffrey working together = 1
∴ the number of days required to finish 1 work by Anthony + Jeffrey together
= 1/15/224
= 1 × 224/15 = 224/15 days
= 14 14/15 days = or 14.933 days
Thus, Anthony and Jeffrey working together will finish the work in 14 14/15 days = or 14.933 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 Anthony = 28 days
And the number of days required to finish the same work by Jeffrey = 32 days
Thus, the number of days required to finish the work Anthony and Jeffrey working together = ?
Here a = 28 days
And, b = 32 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Anthony and Jeffrey working together
= 28 × 32/28 + 32 days
= 896/60 days
= 896 ÷ 4/60 ÷ 4 = 224/15 days
= 14 14/15 days or 14.933
Thus, Anthony and Jeffrey together will finish the work in 14 14/15 days or 14.933 days Answer
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