Question : If Sandra can finish the work in 31 days and Gary can finish the same work in 34 days, then in how many days both can finish the work together?
Correct Answer 16 14/65 days or 16.215 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Sandra = 31 days
And, the number of days to finish the same work by Gary = 34 days
Thus, the number of days to finish the work by Sandra and Gary together = ?
Here,
∵ In 31 days the work done by Sandra = 1
∴ In 1 day, the work done by Sandra = 1/31 part
Similarly,
∵ In 34 days the work done by Gary = 1
∴ In 1 day, the work done by Gary = 1/34 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
= 1/31 + 1/34
= 34 + 31/1054
= 65/1054 part of work
This means in 1 day, 65/1054 part of work is done by Sandra and Gary working together.
Now, the number of days required to finish 65/1054 part of work by Sandra + Gary working together = 1
∴ the number of days required to finish 1 work by Sandra + Gary together
= 1/65/1054
= 1 × 1054/65 = 1054/65 days
= 16 14/65 days = or 16.215 days
Thus, Sandra and Gary working together will finish the work in 16 14/65 days = or 16.215 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 = 31 days
And the number of days required to finish the same work by Gary = 34 days
Thus, the number of days required to finish the work Sandra and Gary working together = ?
Here a = 31 days
And, b = 34 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Sandra and Gary working together
= 31 × 34/31 + 34 days
= 1054/65 days
= 16 14/65 days or 16.215
Thus, Sandra and Gary together will finish the work in 16 14/65 days or 16.215 days Answer
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