Question:
If Sandra can finish the work in 34 days and Gary can finish the same work in 39 days, then in how many days both can finish the work together?
Correct Answer
18 12/73 days or 18.164 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Sandra = 34 days
And, the number of days to finish the same work by Gary = 39 days
Thus, the number of days to finish the work by Sandra and Gary together = ?
Here,
∵ In 34 days the work done by Sandra = 1
∴ In 1 day, the work done by Sandra = 1/34 part
Similarly,
∵ In 39 days the work done by Gary = 1
∴ In 1 day, the work done by Gary = 1/39 part
Now, in 1 day, the work done by Sandra and Gary together
= In 1 day work done by Sandra + In 1 day the work done by Gary
= 1/34 + 1/39
= 39 + 34/1326
= 73/1326 part of work
This means in 1 day, 73/1326 part of work is done by Sandra and Gary working together.
Now, the number of days required to finish 73/1326 part of work by Sandra + Gary working together = 1
∴ the number of days required to finish 1 work by Sandra + Gary together
= 1/73/1326
= 1 × 1326/73 = 1326/73 days
= 18 12/73 days = or 18.164 days
Thus, Sandra and Gary working together will finish the work in 18 12/73 days = or 18.164 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 Sandra = 34 days
And the number of days required to finish the same work by Gary = 39 days
Thus, the number of days required to finish the work Sandra and Gary working together = ?
Here a = 34 days
And, b = 39 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Sandra and Gary working together
= 34 × 39/34 + 39 days
= 1326/73 days
= 18 12/73 days or 18.164
Thus, Sandra and Gary together will finish the work in 18 12/73 days or 18.164 days Answer
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