Question:
If John can finish the work in 28 days and Richard can finish the same work in 44 days, then in how many days both can finish the work together?
Correct Answer
17 1/9 days or 17.111 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by John = 28 days
And, the number of days to finish the same work by Richard = 44 days
Thus, the number of days to finish the work by John and Richard together = ?
Here,
∵ In 28 days the work done by John = 1
∴ In 1 day, the work done by John = 1/28 part
Similarly,
∵ In 44 days the work done by Richard = 1
∴ In 1 day, the work done by Richard = 1/44 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
= 1/28 + 1/44
= 11 + 7/308
= 18/308 part of work
= 18 ÷ 2/308 ÷ 2 part of work
= 9/154 part of work
This means, in 1 day, 9/154 part of the work is done by John and Richard together.
Now, the number of days required to finish 9/154 part of work by John + Richard working together = 1
∴ the number of days required to finish 1 work by John + Richard together
= 1/9/154
= 1 × 154/9 = 154/9 days
= 17 1/9 days = or 17.111 days
Thus, John and Richard working together will finish the work in 17 1/9 days = or 17.111 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 = 28 days
And the number of days required to finish the same work by Richard = 44 days
Thus, the number of days required to finish the work John and Richard working together = ?
Here a = 28 days
And, b = 44 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when John and Richard working together
= 28 × 44/28 + 44 days
= 1232/72 days
= 1232 ÷ 8/72 ÷ 8 = 154/9 days
= 17 1/9 days or 17.111
Thus, John and Richard together will finish the work in 17 1/9 days or 17.111 days Answer
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