Question:
If Christine can finish the work in 90 days and Juan can finish the same work in 95 days, then in how many days both can finish the work together?
Correct Answer
46 8/37 days or 46.216 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Christine = 90 days
And, the number of days to finish the same work by Juan = 95 days
Thus, the number of days to finish the work by Christine and Juan together = ?
Here,
∵ In 90 days the work done by Christine = 1
∴ In 1 day, the work done by Christine = 1/90 part
Similarly,
∵ In 95 days the work done by Juan = 1
∴ In 1 day, the work done by Juan = 1/95 part
Now, in 1 day, the work done by Christine and Juan together
= In 1 day work done by Christine + In 1 day the work done by Juan
= 1/90 + 1/95
= 19 + 18/1710
= 37/1710 part of work
This means in 1 day, 37/1710 part of work is done by Christine and Juan working together.
Now, the number of days required to finish 37/1710 part of work by Christine + Juan working together = 1
∴ the number of days required to finish 1 work by Christine + Juan together
= 1/37/1710
= 1 × 1710/37 = 1710/37 days
= 46 8/37 days = or 46.216 days
Thus, Christine and Juan working together will finish the work in 46 8/37 days = or 46.216 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 Christine = 90 days
And the number of days required to finish the same work by Juan = 95 days
Thus, the number of days required to finish the work Christine and Juan working together = ?
Here a = 90 days
And, b = 95 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Christine and Juan working together
= 90 × 95/90 + 95 days
= 8550/185 days
= 8550 ÷ 5/185 ÷ 5 = 1710/37 days
= 46 8/37 days or 46.216
Thus, Christine and Juan together will finish the work in 46 8/37 days or 46.216 days Answer
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