Question : If Robert can finish the work in 7 days and David can finish the same work in 12 days, then in how many days both can finish the work together?
Correct Answer 4 8/19 days or 4.421 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Robert = 7 days
And, the number of days to finish the same work by David = 12 days
Thus, the number of days to finish the work by Robert and David together = ?
Here,
∵ In 7 days the work done by Robert = 1
∴ In 1 day, the work done by Robert = 1/7 part
Similarly,
∵ In 12 days the work done by David = 1
∴ In 1 day, the work done by David = 1/12 part
Now, in 1 day, the work done by Robert and David together
= In 1 day work done by Robert + In 1 day the work done by David
= 1/7 + 1/12
= 12 + 7/84
= 19/84 part of work
This means in 1 day, 19/84 part of work is done by Robert and David working together.
Now, the number of days required to finish 19/84 part of work by Robert + David working together = 1
∴ the number of days required to finish 1 work by Robert + David together
= 1/19/84
= 1 × 84/19 = 84/19 days
= 4 8/19 days = or 4.421 days
Thus, Robert and David working together will finish the work in 4 8/19 days = or 4.421 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 Robert = 7 days
And the number of days required to finish the same work by David = 12 days
Thus, the number of days required to finish the work Robert and David working together = ?
Here a = 7 days
And, b = 12 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Robert and David working together
= 7 × 12/7 + 12 days
= 84/19 days
= 4 8/19 days or 4.421
Thus, Robert and David together will finish the work in 4 8/19 days or 4.421 days Answer
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