Question : If Kenneth can finish the work in 42 days and Gregory can finish the same work in 45 days, then in how many days both can finish the work together?
Correct Answer 21 21/29 days or 21.724 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Kenneth = 42 days
And, the number of days to finish the same work by Gregory = 45 days
Thus, the number of days to finish the work by Kenneth and Gregory together = ?
Here,
∵ In 42 days the work done by Kenneth = 1
∴ In 1 day, the work done by Kenneth = 1/42 part
Similarly,
∵ In 45 days the work done by Gregory = 1
∴ In 1 day, the work done by Gregory = 1/45 part
Now, in 1 day, the work done by Kenneth and Gregory together
= In 1 day work done by Kenneth + In 1 day the work done by Gregory
= 1/42 + 1/45
= 15 + 14/630
= 29/630 part of work
This means in 1 day, 29/630 part of work is done by Kenneth and Gregory working together.
Now, the number of days required to finish 29/630 part of work by Kenneth + Gregory working together = 1
∴ the number of days required to finish 1 work by Kenneth + Gregory together
= 1/29/630
= 1 × 630/29 = 630/29 days
= 21 21/29 days = or 21.724 days
Thus, Kenneth and Gregory working together will finish the work in 21 21/29 days = or 21.724 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 Kenneth = 42 days
And the number of days required to finish the same work by Gregory = 45 days
Thus, the number of days required to finish the work Kenneth and Gregory working together = ?
Here a = 42 days
And, b = 45 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Kenneth and Gregory working together
= 42 × 45/42 + 45 days
= 1890/87 days
= 1890 ÷ 3/87 ÷ 3 = 630/29 days
= 21 21/29 days or 21.724
Thus, Kenneth and Gregory together will finish the work in 21 21/29 days or 21.724 days Answer
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