Question : If Susan can finish the work in 18 days and Donald can finish the same work in 23 days, then in how many days both can finish the work together?
Correct Answer 10 4/41 days or 10.098 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Susan = 18 days
And, the number of days to finish the same work by Donald = 23 days
Thus, the number of days to finish the work by Susan and Donald together = ?
Here,
∵ In 18 days the work done by Susan = 1
∴ In 1 day, the work done by Susan = 1/18 part
Similarly,
∵ In 23 days the work done by Donald = 1
∴ In 1 day, the work done by Donald = 1/23 part
Now, in 1 day, the work done by Susan and Donald together
= In 1 day work done by Susan + In 1 day the work done by Donald
= 1/18 + 1/23
= 23 + 18/414
= 41/414 part of work
This means in 1 day, 41/414 part of work is done by Susan and Donald working together.
Now, the number of days required to finish 41/414 part of work by Susan + Donald working together = 1
∴ the number of days required to finish 1 work by Susan + Donald together
= 1/41/414
= 1 × 414/41 = 414/41 days
= 10 4/41 days = or 10.098 days
Thus, Susan and Donald working together will finish the work in 10 4/41 days = or 10.098 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 Susan = 18 days
And the number of days required to finish the same work by Donald = 23 days
Thus, the number of days required to finish the work Susan and Donald working together = ?
Here a = 18 days
And, b = 23 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Susan and Donald working together
= 18 × 23/18 + 23 days
= 414/41 days
= 10 4/41 days or 10.098
Thus, Susan and Donald together will finish the work in 10 4/41 days or 10.098 days Answer
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