Question:
If Linda can finish the work in 9 days and Charles can finish the same work in 12 days, then in how many days both can finish the work together?
Correct Answer
5 1/7 days or 5.143 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Linda = 9 days
And, the number of days to finish the same work by Charles = 12 days
Thus, the number of days to finish the work by Linda and Charles together = ?
Here,
∵ In 9 days the work done by Linda = 1
∴ In 1 day, the work done by Linda = 1/9 part
Similarly,
∵ In 12 days the work done by Charles = 1
∴ In 1 day, the work done by Charles = 1/12 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
= 1/9 + 1/12
= 4 + 3/36
= 7/36 part of work
This means in 1 day, 7/36 part of work is done by Linda and Charles working together.
Now, the number of days required to finish 7/36 part of work by Linda + Charles working together = 1
∴ the number of days required to finish 1 work by Linda + Charles together
= 1/7/36
= 1 × 36/7 = 36/7 days
= 5 1/7 days = or 5.143 days
Thus, Linda and Charles working together will finish the work in 5 1/7 days = or 5.143 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 = 9 days
And the number of days required to finish the same work by Charles = 12 days
Thus, the number of days required to finish the work Linda and Charles working together = ?
Here a = 9 days
And, b = 12 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Linda and Charles working together
= 9 × 12/9 + 12 days
= 108/21 days
= 108 ÷ 3/21 ÷ 3 = 36/7 days
= 5 1/7 days or 5.143
Thus, Linda and Charles together will finish the work in 5 1/7 days or 5.143 days Answer
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