Question : Nicholas can finish a work in 69 days. Jonathan can finish the same work in 74 days while Stephen can finish the work in 79 days. How long will it take to finish it if they work together?
Correct Answer 24 9702/16403 days or 24.591 days
Solution & Explanation
Solution
Given,
The number of days required to finish a piece of work by Nicholas = 69 days
And, the number of days required to finish the same work by Jonathan = 74 days
And, the number of days required to finish the same work by Stephen = 79 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 69 days the work is done by Nicholas = 1
∴ The work done by Nicholas in 1 day = 1/69
Similarly,
∵ In 74 days the work is done by Jonathan = 1
∴ The work done by Jonathan in 1 day = 1/74
Similarly,
∵ In 79 days the work is done by Stephen = 1
∴ The work done by Stephen in 1 day = 1/79 part
Now, the work done by Nicholas, Jonathan, and Stephen together in 1 day
= Nicholas's 1 day work + Jonathan's 1 day work + Stephen's 1 day work
= 1/69 + 1/74 + 1/79
= 5846 + 5451 + 5106/403374
= 16403/403374 part of work
This means in 1 day, 16403/403374 part of work is done by Nicholas, Jonathan and Stephen working together.
Now, the number of days required to finish 16403/403374 part of work by Nicholas, Jonathan, and Stephen working together = 1
∴ the number of days required to finish the whole work (1 work) by Nicholas + Jonathan + Stephen together
= 1/16403/403374
= 1 × 403374/16403 = 403374/16403 days
= 24 9702/16403 days = or 24.591 days
Thus, Nicholas, Jonathan, and Stephen working together will finish the total work (1 work) in 24 9702/16403 days = or 24.591 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, B can finish the same work in b days, and C can finish the work in c days
then working together the number of days required to finish the work
= a × b × c/ab + ac + bc 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 Jonathan = 74 days
And the number of days required to finish the work by Stephen = 79 days
Thus, the number of days required to finish the work by Nicholas, Jonathan, and Stephen together = ?
Here a = 69 days
And, b = 74 days
And, c = 79 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Nicholas, Jonathan, and Stephen working together
= 69 × 74 × 79/69 × 74 + 69 × 79 + 74 × 79 days
= 403374/5106 + 5451 + 5846 days
= 403374/16403 days
= 403374/16403 days
= 24 9702/16403 days or 24.591
Thus, Nicholas, Jonathan, and Stephen together will finish the work in 24 9702/16403 days or 24.591 days Answer
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