Question : If Linda can finish the work in 31 days and Charles can finish the same work in 47 days, then in how many days both can finish the work together?
Correct Answer 18 53/78 days or 18.679 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Linda = 31 days
And, the number of days to finish the same work by Charles = 47 days
Thus, the number of days to finish the work by Linda and Charles together = ?
Here,
∵ In 31 days the work done by Linda = 1
∴ In 1 day, the work done by Linda = 1/31 part
Similarly,
∵ In 47 days the work done by Charles = 1
∴ In 1 day, the work done by Charles = 1/47 part
Now, in 1 day, the work done by Linda and Charles together
= In 1 day work done by Linda + In 1 day the work done by Charles
= 1/31 + 1/47
= 47 + 31/1457
= 78/1457 part of work
This means in 1 day, 78/1457 part of work is done by Linda and Charles working together.
Now, the number of days required to finish 78/1457 part of work by Linda + Charles working together = 1
∴ the number of days required to finish 1 work by Linda + Charles together
= 1/78/1457
= 1 × 1457/78 = 1457/78 days
= 18 53/78 days = or 18.679 days
Thus, Linda and Charles working together will finish the work in 18 53/78 days = or 18.679 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 Linda = 31 days
And the number of days required to finish the same work by Charles = 47 days
Thus, the number of days required to finish the work Linda and Charles working together = ?
Here a = 31 days
And, b = 47 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Linda and Charles working together
= 31 × 47/31 + 47 days
= 1457/78 days
= 18 53/78 days or 18.679
Thus, Linda and Charles together will finish the work in 18 53/78 days or 18.679 days Answer
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