Question:
If Andrew can finish the work in 38 days and Scott can finish the same work in 42 days, then in how many days both can finish the work together?
Correct Answer
19 19/20 days or 19.95 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Andrew = 38 days
And, the number of days to finish the same work by Scott = 42 days
Thus, the number of days to finish the work by Andrew and Scott together = ?
Here,
∵ In 38 days the work done by Andrew = 1
∴ In 1 day, the work done by Andrew = 1/38 part
Similarly,
∵ In 42 days the work done by Scott = 1
∴ In 1 day, the work done by Scott = 1/42 part
Now, in 1 day, the work done by Andrew and Scott together
= In 1 day work done by Andrew + In 1 day the work done by Scott
= 1/38 + 1/42
= 21 + 19/798
= 40/798 part of work
= 40 ÷ 2/798 ÷ 2 part of work
= 20/399 part of work
This means, in 1 day, 20/399 part of the work is done by Andrew and Scott together.
Now, the number of days required to finish 20/399 part of work by Andrew + Scott working together = 1
∴ the number of days required to finish 1 work by Andrew + Scott together
= 1/20/399
= 1 × 399/20 = 399/20 days
= 19 19/20 days = or 19.95 days
Thus, Andrew and Scott working together will finish the work in 19 19/20 days = or 19.95 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 Andrew = 38 days
And the number of days required to finish the same work by Scott = 42 days
Thus, the number of days required to finish the work Andrew and Scott working together = ?
Here a = 38 days
And, b = 42 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Andrew and Scott working together
= 38 × 42/38 + 42 days
= 1596/80 days
= 1596 ÷ 4/80 ÷ 4 = 399/20 days
= 19 19/20 days or 19.95
Thus, Andrew and Scott together will finish the work in 19 19/20 days or 19.95 days Answer
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