Question : If John can finish the work in 9 days and Richard can finish the same work in 14 days, then in how many days both can finish the work together?
Correct Answer 5 11/23 days or 5.478 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by John = 9 days
And, the number of days to finish the same work by Richard = 14 days
Thus, the number of days to finish the work by John and Richard together = ?
Here,
∵ In 9 days the work done by John = 1
∴ In 1 day, the work done by John = 1/9 part
Similarly,
∵ In 14 days the work done by Richard = 1
∴ In 1 day, the work done by Richard = 1/14 part
Now, in 1 day, the work done by John and Richard together
= In 1 day work done by John + In 1 day the work done by Richard
= 1/9 + 1/14
= 14 + 9/126
= 23/126 part of work
This means in 1 day, 23/126 part of work is done by John and Richard working together.
Now, the number of days required to finish 23/126 part of work by John + Richard working together = 1
∴ the number of days required to finish 1 work by John + Richard together
= 1/23/126
= 1 × 126/23 = 126/23 days
= 5 11/23 days = or 5.478 days
Thus, John and Richard working together will finish the work in 5 11/23 days = or 5.478 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 John = 9 days
And the number of days required to finish the same work by Richard = 14 days
Thus, the number of days required to finish the work John and Richard working together = ?
Here a = 9 days
And, b = 14 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when John and Richard working together
= 9 × 14/9 + 14 days
= 126/23 days
= 5 11/23 days or 5.478
Thus, John and Richard together will finish the work in 5 11/23 days or 5.478 days Answer
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