Question:
If Angela can finish the work in 70 days and Terry can finish the same work in 75 days, then in how many days both can finish the work together?
Correct Answer
36 6/29 days or 36.207 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Angela = 70 days
And, the number of days to finish the same work by Terry = 75 days
Thus, the number of days to finish the work by Angela and Terry together = ?
Here,
∵ In 70 days the work done by Angela = 1
∴ In 1 day, the work done by Angela = 1/70 part
Similarly,
∵ In 75 days the work done by Terry = 1
∴ In 1 day, the work done by Terry = 1/75 part
Now, in 1 day, the work done by Angela and Terry together
= In 1 day work done by Angela + In 1 day the work done by Terry
= 1/70 + 1/75
= 15 + 14/1050
= 29/1050 part of work
This means in 1 day, 29/1050 part of work is done by Angela and Terry working together.
Now, the number of days required to finish 29/1050 part of work by Angela + Terry working together = 1
∴ the number of days required to finish 1 work by Angela + Terry together
= 1/29/1050
= 1 × 1050/29 = 1050/29 days
= 36 6/29 days = or 36.207 days
Thus, Angela and Terry working together will finish the work in 36 6/29 days = or 36.207 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 Angela = 70 days
And the number of days required to finish the same work by Terry = 75 days
Thus, the number of days required to finish the work Angela and Terry working together = ?
Here a = 70 days
And, b = 75 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Angela and Terry working together
= 70 × 75/70 + 75 days
= 5250/145 days
= 5250 ÷ 5/145 ÷ 5 = 1050/29 days
= 36 6/29 days or 36.207
Thus, Angela and Terry together will finish the work in 36 6/29 days or 36.207 days Answer
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