Question:
If John can finish the work in 6 days and Richard can finish the same work in 10 days, then in how many days both can finish the work together?
Correct Answer
3 3/4 days or 3.75 days
Solution And 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 = 10 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 10 days the work done by Richard = 1
∴ In 1 day, the work done by Richard = 1/10 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 + 1/10
= 5 + 3/30
= 8/30 part of work
= 8 ÷ 2/30 ÷ 2 part of work
= 4/15 part of work
This means, in 1 day, 4/15 part of the work is done by John and Richard together.
Now, the number of days required to finish 4/15 part of work by John + Richard working together = 1
∴ the number of days required to finish 1 work by John + Richard together
= 1/4/15
= 1 × 15/4 = 15/4 days
= 3 3/4 days = or 3.75 days
Thus, John and Richard working together will finish the work in 3 3/4 days = or 3.75 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 = 10 days
Thus, the number of days required to finish the work John and Richard working together = ?
Here a = 6 days
And, b = 10 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 × 10/6 + 10 days
= 60/16 days
= 60 ÷ 4/16 ÷ 4 = 15/4 days
= 3 3/4 days or 3.75
Thus, John and Richard together will finish the work in 3 3/4 days or 3.75 days Answer
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