Question:
If Sarah can finish the work in 22 days and Joshua can finish the same work in 27 days, then in how many days both can finish the work together?
Correct Answer
12 6/49 days or 12.122 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Sarah = 22 days
And, the number of days to finish the same work by Joshua = 27 days
Thus, the number of days to finish the work by Sarah and Joshua together = ?
Here,
∵ In 22 days the work done by Sarah = 1
∴ In 1 day, the work done by Sarah = 1/22 part
Similarly,
∵ In 27 days the work done by Joshua = 1
∴ In 1 day, the work done by Joshua = 1/27 part
Now, in 1 day, the work done by Sarah and Joshua together
= In 1 day work done by Sarah + In 1 day the work done by Joshua
= 1/22 + 1/27
= 27 + 22/594
= 49/594 part of work
This means in 1 day, 49/594 part of work is done by Sarah and Joshua working together.
Now, the number of days required to finish 49/594 part of work by Sarah + Joshua working together = 1
∴ the number of days required to finish 1 work by Sarah + Joshua together
= 1/49/594
= 1 × 594/49 = 594/49 days
= 12 6/49 days = or 12.122 days
Thus, Sarah and Joshua working together will finish the work in 12 6/49 days = or 12.122 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 Sarah = 22 days
And the number of days required to finish the same work by Joshua = 27 days
Thus, the number of days required to finish the work Sarah and Joshua working together = ?
Here a = 22 days
And, b = 27 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Sarah and Joshua working together
= 22 × 27/22 + 27 days
= 594/49 days
= 12 6/49 days or 12.122
Thus, Sarah and Joshua together will finish the work in 12 6/49 days or 12.122 days Answer
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