Question : If Joseph can finish the work in 19 days and Steven can finish the same work in 24 days, then in how many days both can finish the work together?
Correct Answer 10 26/43 days or 10.605 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Joseph = 19 days
And, the number of days to finish the same work by Steven = 24 days
Thus, the number of days to finish the work by Joseph and Steven together = ?
Here,
∵ In 19 days the work done by Joseph = 1
∴ In 1 day, the work done by Joseph = 1/19 part
Similarly,
∵ In 24 days the work done by Steven = 1
∴ In 1 day, the work done by Steven = 1/24 part
Now, in 1 day, the work done by Joseph and Steven together
= In 1 day work done by Joseph + In 1 day the work done by Steven
= 1/19 + 1/24
= 24 + 19/456
= 43/456 part of work
This means in 1 day, 43/456 part of work is done by Joseph and Steven working together.
Now, the number of days required to finish 43/456 part of work by Joseph + Steven working together = 1
∴ the number of days required to finish 1 work by Joseph + Steven together
= 1/43/456
= 1 × 456/43 = 456/43 days
= 10 26/43 days = or 10.605 days
Thus, Joseph and Steven working together will finish the work in 10 26/43 days = or 10.605 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 Joseph = 19 days
And the number of days required to finish the same work by Steven = 24 days
Thus, the number of days required to finish the work Joseph and Steven working together = ?
Here a = 19 days
And, b = 24 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Joseph and Steven working together
= 19 × 24/19 + 24 days
= 456/43 days
= 10 26/43 days or 10.605
Thus, Joseph and Steven together will finish the work in 10 26/43 days or 10.605 days Answer
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