Question:
If Eric can finish the work in 71 days and Gerald can finish the same work in 76 days, then in how many days both can finish the work together?
Correct Answer
36 104/147 days or 36.707 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Eric = 71 days
And, the number of days to finish the same work by Gerald = 76 days
Thus, the number of days to finish the work by Eric and Gerald together = ?
Here,
∵ In 71 days the work done by Eric = 1
∴ In 1 day, the work done by Eric = 1/71 part
Similarly,
∵ In 76 days the work done by Gerald = 1
∴ In 1 day, the work done by Gerald = 1/76 part
Now, in 1 day, the work done by Eric and Gerald together
= In 1 day work done by Eric + In 1 day the work done by Gerald
= 1/71 + 1/76
= 76 + 71/5396
= 147/5396 part of work
This means in 1 day, 147/5396 part of work is done by Eric and Gerald working together.
Now, the number of days required to finish 147/5396 part of work by Eric + Gerald working together = 1
∴ the number of days required to finish 1 work by Eric + Gerald together
= 1/147/5396
= 1 × 5396/147 = 5396/147 days
= 36 104/147 days = or 36.707 days
Thus, Eric and Gerald working together will finish the work in 36 104/147 days = or 36.707 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 Eric = 71 days
And the number of days required to finish the same work by Gerald = 76 days
Thus, the number of days required to finish the work Eric and Gerald working together = ?
Here a = 71 days
And, b = 76 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Eric and Gerald working together
= 71 × 76/71 + 76 days
= 5396/147 days
= 36 104/147 days or 36.707
Thus, Eric and Gerald together will finish the work in 36 104/147 days or 36.707 days Answer
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