Question : If Myra can finish the work in 15 days and Sophia can finish the same work in 20 days, then in how many days they both can finish the work working together?
Correct Answer 8 4/7 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Myra = 15 days
And, the number of days to finish the same work by Sophia = 20 days
Thus, the number of days to finish the work by Myra and Sophia working together = ?
Here, ∵ In 15 days the work done by Myra = 1
∴ In 1 day, the work done by Myra = 1/15 part
Similarly, ∵ In 20 days the work done by Sophia = 1
∴ In 1 day, the work done by Sophia = 1/20 part
Now, in 1 day, the work done by Myra and Sophia working together
= In 1 day work done by Myra + In 1 day the work done by Sophia
= 1/15 + 1/20
= 4 + 3/60
= 7/60 part of work
This means in 1 day, 7/60 part of work is done by Myra and Sophia working together.
Now, the number of days required to finish 5/60 part of work by Myra + Sophia working together = 1
∴ the number of days required to finish 1 work by Myra + Sophia working together
= 1/7/60
= 1 × 60/7 days = 60/7 days
= 8 4/7 days
Thus, Myra and Sophia working together will finish the work in 8 4/7 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 to finish the work by Myra = 15 days
And, the number of days to finish the same work by Sophia = 20 days
Thus, the number of days to finish the work by Myra and Sophia working together = ?
Here "a" = 15 days
And, "b" = 20 days
Thus, using formula a × b/a + b days
The number of days require to finish the work when Myra and Sophia working together
= 15 × 20/15 + 20 days
= 300/35 days
= 60 × 5/7 × 5 = 60/7 days
= 8 4/7 days
Thus, Myra and Sophia working together will finish the work in 8 4/7 days Answer
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