Question : If Steven can finish the work in 34 days and Jonathan can finish the same work in 38 days, then in how many days both can finish the work together?
Correct Answer 17 17/18 days or 17.944 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Steven = 34 days
And, the number of days to finish the same work by Jonathan = 38 days
Thus, the number of days to finish the work by Steven and Jonathan together = ?
Here,
∵ In 34 days the work done by Steven = 1
∴ In 1 day, the work done by Steven = 1/34 part
Similarly,
∵ In 38 days the work done by Jonathan = 1
∴ In 1 day, the work done by Jonathan = 1/38 part
Now, in 1 day, the work done by Steven and Jonathan together
= In 1 day work done by Steven + In 1 day the work done by Jonathan
= 1/34 + 1/38
= 19 + 17/646
= 36/646 part of work
= 36 ÷ 2/646 ÷ 2 part of work
= 18/323 part of work
This means, in 1 day, 18/323 part of the work is done by Steven and Jonathan together.
Now, the number of days required to finish 18/323 part of work by Steven + Jonathan working together = 1
∴ the number of days required to finish 1 work by Steven + Jonathan together
= 1/18/323
= 1 × 323/18 = 323/18 days
= 17 17/18 days = or 17.944 days
Thus, Steven and Jonathan working together will finish the work in 17 17/18 days = or 17.944 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 Steven = 34 days
And the number of days required to finish the same work by Jonathan = 38 days
Thus, the number of days required to finish the work Steven and Jonathan working together = ?
Here a = 34 days
And, b = 38 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Steven and Jonathan working together
= 34 × 38/34 + 38 days
= 1292/72 days
= 1292 ÷ 4/72 ÷ 4 = 323/18 days
= 17 17/18 days or 17.944
Thus, Steven and Jonathan together will finish the work in 17 17/18 days or 17.944 days Answer
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