Question : If Patricia can finish the work in 27 days and William can finish the same work in 43 days, then in how many days both can finish the work together?
Correct Answer 16 41/70 days or 16.586 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Patricia = 27 days
And, the number of days to finish the same work by William = 43 days
Thus, the number of days to finish the work by Patricia and William together = ?
Here,
∵ In 27 days the work done by Patricia = 1
∴ In 1 day, the work done by Patricia = 1/27 part
Similarly,
∵ In 43 days the work done by William = 1
∴ In 1 day, the work done by William = 1/43 part
Now, in 1 day, the work done by Patricia and William together
= In 1 day work done by Patricia + In 1 day the work done by William
= 1/27 + 1/43
= 43 + 27/1161
= 70/1161 part of work
This means in 1 day, 70/1161 part of work is done by Patricia and William working together.
Now, the number of days required to finish 70/1161 part of work by Patricia + William working together = 1
∴ the number of days required to finish 1 work by Patricia + William together
= 1/70/1161
= 1 × 1161/70 = 1161/70 days
= 16 41/70 days = or 16.586 days
Thus, Patricia and William working together will finish the work in 16 41/70 days = or 16.586 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 Patricia = 27 days
And the number of days required to finish the same work by William = 43 days
Thus, the number of days required to finish the work Patricia and William working together = ?
Here a = 27 days
And, b = 43 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Patricia and William working together
= 27 × 43/27 + 43 days
= 1161/70 days
= 16 41/70 days or 16.586
Thus, Patricia and William together will finish the work in 16 41/70 days or 16.586 days Answer
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