Question:
If Robert can finish the work in 26 days and David can finish the same work in 42 days, then in how many days both can finish the work together?
Correct Answer
16 1/17 days or 16.059 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Robert = 26 days
And, the number of days to finish the same work by David = 42 days
Thus, the number of days to finish the work by Robert and David together = ?
Here,
∵ In 26 days the work done by Robert = 1
∴ In 1 day, the work done by Robert = 1/26 part
Similarly,
∵ In 42 days the work done by David = 1
∴ In 1 day, the work done by David = 1/42 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
= 1/26 + 1/42
= 21 + 13/546
= 34/546 part of work
= 34 ÷ 2/546 ÷ 2 part of work
= 17/273 part of work
This means, in 1 day, 17/273 part of the work is done by Robert and David together.
Now, the number of days required to finish 17/273 part of work by Robert + David working together = 1
∴ the number of days required to finish 1 work by Robert + David together
= 1/17/273
= 1 × 273/17 = 273/17 days
= 16 1/17 days = or 16.059 days
Thus, Robert and David working together will finish the work in 16 1/17 days = or 16.059 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 = 26 days
And the number of days required to finish the same work by David = 42 days
Thus, the number of days required to finish the work Robert and David working together = ?
Here a = 26 days
And, b = 42 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Robert and David working together
= 26 × 42/26 + 42 days
= 1092/68 days
= 1092 ÷ 4/68 ÷ 4 = 273/17 days
= 16 1/17 days or 16.059
Thus, Robert and David together will finish the work in 16 1/17 days or 16.059 days Answer
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