Question : If Larry can finish the work in 77 days and Lawrence can finish the same work in 82 days, then in how many days both can finish the work together?
Correct Answer 39 113/159 days or 39.711 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Larry = 77 days
And, the number of days to finish the same work by Lawrence = 82 days
Thus, the number of days to finish the work by Larry and Lawrence together = ?
Here,
∵ In 77 days the work done by Larry = 1
∴ In 1 day, the work done by Larry = 1/77 part
Similarly,
∵ In 82 days the work done by Lawrence = 1
∴ In 1 day, the work done by Lawrence = 1/82 part
Now, in 1 day, the work done by Larry and Lawrence together
= In 1 day work done by Larry + In 1 day the work done by Lawrence
= 1/77 + 1/82
= 82 + 77/6314
= 159/6314 part of work
This means in 1 day, 159/6314 part of work is done by Larry and Lawrence working together.
Now, the number of days required to finish 159/6314 part of work by Larry + Lawrence working together = 1
∴ the number of days required to finish 1 work by Larry + Lawrence together
= 1/159/6314
= 1 × 6314/159 = 6314/159 days
= 39 113/159 days = or 39.711 days
Thus, Larry and Lawrence working together will finish the work in 39 113/159 days = or 39.711 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 Larry = 77 days
And the number of days required to finish the same work by Lawrence = 82 days
Thus, the number of days required to finish the work Larry and Lawrence working together = ?
Here a = 77 days
And, b = 82 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Larry and Lawrence working together
= 77 × 82/77 + 82 days
= 6314/159 days
= 39 113/159 days or 39.711
Thus, Larry and Lawrence together will finish the work in 39 113/159 days or 39.711 days Answer
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