Question:
If Nicholas can finish the work in 69 days and Roger can finish the same work in 74 days, then in how many days both can finish the work together?
Correct Answer
35 101/143 days or 35.706 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Nicholas = 69 days
And, the number of days to finish the same work by Roger = 74 days
Thus, the number of days to finish the work by Nicholas and Roger together = ?
Here,
∵ In 69 days the work done by Nicholas = 1
∴ In 1 day, the work done by Nicholas = 1/69 part
Similarly,
∵ In 74 days the work done by Roger = 1
∴ In 1 day, the work done by Roger = 1/74 part
Now, in 1 day, the work done by Nicholas and Roger together
= In 1 day work done by Nicholas + In 1 day the work done by Roger
= 1/69 + 1/74
= 74 + 69/5106
= 143/5106 part of work
This means in 1 day, 143/5106 part of work is done by Nicholas and Roger working together.
Now, the number of days required to finish 143/5106 part of work by Nicholas + Roger working together = 1
∴ the number of days required to finish 1 work by Nicholas + Roger together
= 1/143/5106
= 1 × 5106/143 = 5106/143 days
= 35 101/143 days = or 35.706 days
Thus, Nicholas and Roger working together will finish the work in 35 101/143 days = or 35.706 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 Nicholas = 69 days
And the number of days required to finish the same work by Roger = 74 days
Thus, the number of days required to finish the work Nicholas and Roger working together = ?
Here a = 69 days
And, b = 74 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Nicholas and Roger working together
= 69 × 74/69 + 74 days
= 5106/143 days
= 35 101/143 days or 35.706
Thus, Nicholas and Roger together will finish the work in 35 101/143 days or 35.706 days Answer
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