Question : If Michael can finish the work in 30 days and Thomas can finish the same work in 46 days, then in how many days both can finish the work together?
Correct Answer 18 3/19 days or 18.158 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Michael = 30 days
And, the number of days to finish the same work by Thomas = 46 days
Thus, the number of days to finish the work by Michael and Thomas together = ?
Here,
∵ In 30 days the work done by Michael = 1
∴ In 1 day, the work done by Michael = 1/30 part
Similarly,
∵ In 46 days the work done by Thomas = 1
∴ In 1 day, the work done by Thomas = 1/46 part
Now, in 1 day, the work done by Michael and Thomas together
= In 1 day work done by Michael + In 1 day the work done by Thomas
= 1/30 + 1/46
= 23 + 15/690
= 38/690 part of work
= 38 ÷ 2/690 ÷ 2 part of work
= 19/345 part of work
This means, in 1 day, 19/345 part of the work is done by Michael and Thomas together.
Now, the number of days required to finish 19/345 part of work by Michael + Thomas working together = 1
∴ the number of days required to finish 1 work by Michael + Thomas together
= 1/19/345
= 1 × 345/19 = 345/19 days
= 18 3/19 days = or 18.158 days
Thus, Michael and Thomas working together will finish the work in 18 3/19 days = or 18.158 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 Michael = 30 days
And the number of days required to finish the same work by Thomas = 46 days
Thus, the number of days required to finish the work Michael and Thomas working together = ?
Here a = 30 days
And, b = 46 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Michael and Thomas working together
= 30 × 46/30 + 46 days
= 1380/76 days
= 1380 ÷ 4/76 ÷ 4 = 345/19 days
= 18 3/19 days or 18.158
Thus, Michael and Thomas together will finish the work in 18 3/19 days or 18.158 days Answer
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