Question : If Stephen can finish the work in 75 days and Carl can finish the same work in 80 days, then in how many days both can finish the work together?
Correct Answer 38 22/31 days or 38.71 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Stephen = 75 days
And, the number of days to finish the same work by Carl = 80 days
Thus, the number of days to finish the work by Stephen and Carl together = ?
Here,
∵ In 75 days the work done by Stephen = 1
∴ In 1 day, the work done by Stephen = 1/75 part
Similarly,
∵ In 80 days the work done by Carl = 1
∴ In 1 day, the work done by Carl = 1/80 part
Now, in 1 day, the work done by Stephen and Carl together
= In 1 day work done by Stephen + In 1 day the work done by Carl
= 1/75 + 1/80
= 16 + 15/1200
= 31/1200 part of work
This means in 1 day, 31/1200 part of work is done by Stephen and Carl working together.
Now, the number of days required to finish 31/1200 part of work by Stephen + Carl working together = 1
∴ the number of days required to finish 1 work by Stephen + Carl together
= 1/31/1200
= 1 × 1200/31 = 1200/31 days
= 38 22/31 days = or 38.71 days
Thus, Stephen and Carl working together will finish the work in 38 22/31 days = or 38.71 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 Stephen = 75 days
And the number of days required to finish the same work by Carl = 80 days
Thus, the number of days required to finish the work Stephen and Carl working together = ?
Here a = 75 days
And, b = 80 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Stephen and Carl working together
= 75 × 80/75 + 80 days
= 6000/155 days
= 6000 ÷ 5/155 ÷ 5 = 1200/31 days
= 38 22/31 days or 38.71
Thus, Stephen and Carl together will finish the work in 38 22/31 days or 38.71 days Answer
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