Question:
If Sharon can finish the work in 60 days and Zachary can finish the same work in 65 days, then in how many days both can finish the work together?
Correct Answer
31 1/5 days or 31.2 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Sharon = 60 days
And, the number of days to finish the same work by Zachary = 65 days
Thus, the number of days to finish the work by Sharon and Zachary together = ?
Here,
∵ In 60 days the work done by Sharon = 1
∴ In 1 day, the work done by Sharon = 1/60 part
Similarly,
∵ In 65 days the work done by Zachary = 1
∴ In 1 day, the work done by Zachary = 1/65 part
Now, in 1 day, the work done by Sharon and Zachary together
= In 1 day work done by Sharon + In 1 day the work done by Zachary
= 1/60 + 1/65
= 13 + 12/780
= 25/780 part of work
= 25 ÷ 5/780 ÷ 5 part of work
= 5/156 part of work
This means, in 1 day, 5/156 part of the work is done by Sharon and Zachary together.
Now, the number of days required to finish 5/156 part of work by Sharon + Zachary working together = 1
∴ the number of days required to finish 1 work by Sharon + Zachary together
= 1/5/156
= 1 × 156/5 = 156/5 days
= 31 1/5 days = or 31.2 days
Thus, Sharon and Zachary working together will finish the work in 31 1/5 days = or 31.2 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 Sharon = 60 days
And the number of days required to finish the same work by Zachary = 65 days
Thus, the number of days required to finish the work Sharon and Zachary working together = ?
Here a = 60 days
And, b = 65 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Sharon and Zachary working together
= 60 × 65/60 + 65 days
= 3900/125 days
= 3900 ÷ 25/125 ÷ 25 = 156/5 days
= 31 1/5 days or 31.2
Thus, Sharon and Zachary together will finish the work in 31 1/5 days or 31.2 days Answer
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