Question : If William can finish the work in 34 days and Matthew can finish the same work in 50 days, then in how many days both can finish the work together?
Correct Answer 20 5/21 days or 20.238 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by William = 34 days
And, the number of days to finish the same work by Matthew = 50 days
Thus, the number of days to finish the work by William and Matthew together = ?
Here,
∵ In 34 days the work done by William = 1
∴ In 1 day, the work done by William = 1/34 part
Similarly,
∵ In 50 days the work done by Matthew = 1
∴ In 1 day, the work done by Matthew = 1/50 part
Now, in 1 day, the work done by William and Matthew together
= In 1 day work done by William + In 1 day the work done by Matthew
= 1/34 + 1/50
= 25 + 17/850
= 42/850 part of work
= 42 ÷ 2/850 ÷ 2 part of work
= 21/425 part of work
This means, in 1 day, 21/425 part of the work is done by William and Matthew together.
Now, the number of days required to finish 21/425 part of work by William + Matthew working together = 1
∴ the number of days required to finish 1 work by William + Matthew together
= 1/21/425
= 1 × 425/21 = 425/21 days
= 20 5/21 days = or 20.238 days
Thus, William and Matthew working together will finish the work in 20 5/21 days = or 20.238 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 William = 34 days
And the number of days required to finish the same work by Matthew = 50 days
Thus, the number of days required to finish the work William and Matthew working together = ?
Here a = 34 days
And, b = 50 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when William and Matthew working together
= 34 × 50/34 + 50 days
= 1700/84 days
= 1700 ÷ 4/84 ÷ 4 = 425/21 days
= 20 5/21 days or 20.238
Thus, William and Matthew together will finish the work in 20 5/21 days or 20.238 days Answer
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