Question : If Carol can finish the work in 43 days and Alexander can finish the same work in 47 days, then in how many days both can finish the work together?
Correct Answer 22 41/90 days or 22.456 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Carol = 43 days
And, the number of days to finish the same work by Alexander = 47 days
Thus, the number of days to finish the work by Carol and Alexander together = ?
Here,
∵ In 43 days the work done by Carol = 1
∴ In 1 day, the work done by Carol = 1/43 part
Similarly,
∵ In 47 days the work done by Alexander = 1
∴ In 1 day, the work done by Alexander = 1/47 part
Now, in 1 day, the work done by Carol and Alexander together
= In 1 day work done by Carol + In 1 day the work done by Alexander
= 1/43 + 1/47
= 47 + 43/2021
= 90/2021 part of work
This means in 1 day, 90/2021 part of work is done by Carol and Alexander working together.
Now, the number of days required to finish 90/2021 part of work by Carol + Alexander working together = 1
∴ the number of days required to finish 1 work by Carol + Alexander together
= 1/90/2021
= 1 × 2021/90 = 2021/90 days
= 22 41/90 days = or 22.456 days
Thus, Carol and Alexander working together will finish the work in 22 41/90 days = or 22.456 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 Carol = 43 days
And the number of days required to finish the same work by Alexander = 47 days
Thus, the number of days required to finish the work Carol and Alexander working together = ?
Here a = 43 days
And, b = 47 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Carol and Alexander working together
= 43 × 47/43 + 47 days
= 2021/90 days
= 22 41/90 days or 22.456
Thus, Carol and Alexander together will finish the work in 22 41/90 days or 22.456 days Answer
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