Question : If John can finish the work in 6 days and Richard can finish the same work in 9 days, then in how many days both can finish the work together?
Correct Answer 3 3/5 days or 3.6 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by John = 6 days
And, the number of days to finish the same work by Richard = 9 days
Thus, the number of days to finish the work by John and Richard together = ?
Here,
∵ In 6 days the work done by John = 1
∴ In 1 day, the work done by John = 1/6 part
Similarly,
∵ In 9 days the work done by Richard = 1
∴ In 1 day, the work done by Richard = 1/9 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
= 1/6 + 1/9
= 3 + 2/18
= 5/18 part of work
This means in 1 day, 5/18 part of work is done by John and Richard working together.
Now, the number of days required to finish 5/18 part of work by John + Richard working together = 1
∴ the number of days required to finish 1 work by John + Richard together
= 1/5/18
= 1 × 18/5 = 18/5 days
= 3 3/5 days = or 3.6 days
Thus, John and Richard working together will finish the work in 3 3/5 days = or 3.6 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 = 6 days
And the number of days required to finish the same work by Richard = 9 days
Thus, the number of days required to finish the work John and Richard working together = ?
Here a = 6 days
And, b = 9 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when John and Richard working together
= 6 × 9/6 + 9 days
= 54/15 days
= 54 ÷ 3/15 ÷ 3 = 18/5 days
= 3 3/5 days or 3.6
Thus, John and Richard together will finish the work in 3 3/5 days or 3.6 days Answer
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