Question : If Jessica can finish the work in 17 days and Paul can finish the same work in 21 days, then in how many days both can finish the work together?
Correct Answer 9 15/38 days or 9.395 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Jessica = 17 days
And, the number of days to finish the same work by Paul = 21 days
Thus, the number of days to finish the work by Jessica and Paul together = ?
Here,
∵ In 17 days the work done by Jessica = 1
∴ In 1 day, the work done by Jessica = 1/17 part
Similarly,
∵ In 21 days the work done by Paul = 1
∴ In 1 day, the work done by Paul = 1/21 part
Now, in 1 day, the work done by Jessica and Paul together
= In 1 day work done by Jessica + In 1 day the work done by Paul
= 1/17 + 1/21
= 21 + 17/357
= 38/357 part of work
This means in 1 day, 38/357 part of work is done by Jessica and Paul working together.
Now, the number of days required to finish 38/357 part of work by Jessica + Paul working together = 1
∴ the number of days required to finish 1 work by Jessica + Paul together
= 1/38/357
= 1 × 357/38 = 357/38 days
= 9 15/38 days = or 9.395 days
Thus, Jessica and Paul working together will finish the work in 9 15/38 days = or 9.395 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 Jessica = 17 days
And the number of days required to finish the same work by Paul = 21 days
Thus, the number of days required to finish the work Jessica and Paul working together = ?
Here a = 17 days
And, b = 21 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Jessica and Paul working together
= 17 × 21/17 + 21 days
= 357/38 days
= 9 15/38 days or 9.395
Thus, Jessica and Paul together will finish the work in 9 15/38 days or 9.395 days Answer
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