Question : If Mark can finish the work in 30 days and Jacob can finish the same work in 34 days, then in how many days both can finish the work together?
Correct Answer 15 15/16 days or 15.938 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Mark = 30 days
And, the number of days to finish the same work by Jacob = 34 days
Thus, the number of days to finish the work by Mark and Jacob together = ?
Here,
∵ In 30 days the work done by Mark = 1
∴ In 1 day, the work done by Mark = 1/30 part
Similarly,
∵ In 34 days the work done by Jacob = 1
∴ In 1 day, the work done by Jacob = 1/34 part
Now, in 1 day, the work done by Mark and Jacob together
= In 1 day work done by Mark + In 1 day the work done by Jacob
= 1/30 + 1/34
= 17 + 15/510
= 32/510 part of work
= 32 ÷ 2/510 ÷ 2 part of work
= 16/255 part of work
This means, in 1 day, 16/255 part of the work is done by Mark and Jacob together.
Now, the number of days required to finish 16/255 part of work by Mark + Jacob working together = 1
∴ the number of days required to finish 1 work by Mark + Jacob together
= 1/16/255
= 1 × 255/16 = 255/16 days
= 15 15/16 days = or 15.938 days
Thus, Mark and Jacob working together will finish the work in 15 15/16 days = or 15.938 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 Mark = 30 days
And the number of days required to finish the same work by Jacob = 34 days
Thus, the number of days required to finish the work Mark and Jacob working together = ?
Here a = 30 days
And, b = 34 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Mark and Jacob working together
= 30 × 34/30 + 34 days
= 1020/64 days
= 1020 ÷ 4/64 ÷ 4 = 255/16 days
= 15 15/16 days or 15.938
Thus, Mark and Jacob together will finish the work in 15 15/16 days or 15.938 days Answer
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