Question:
If Ronald can finish the work in 55 days and Jose can finish the same work in 60 days, then in how many days both can finish the work together?
Correct Answer
28 16/23 days or 28.696 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by Ronald = 55 days
And, the number of days to finish the same work by Jose = 60 days
Thus, the number of days to finish the work by Ronald and Jose together = ?
Here,
∵ In 55 days the work done by Ronald = 1
∴ In 1 day, the work done by Ronald = 1/55 part
Similarly,
∵ In 60 days the work done by Jose = 1
∴ In 1 day, the work done by Jose = 1/60 part
Now, in 1 day, the work done by Ronald and Jose together
= In 1 day work done by Ronald + In 1 day the work done by Jose
= 1/55 + 1/60
= 12 + 11/660
= 23/660 part of work
This means in 1 day, 23/660 part of work is done by Ronald and Jose working together.
Now, the number of days required to finish 23/660 part of work by Ronald + Jose working together = 1
∴ the number of days required to finish 1 work by Ronald + Jose together
= 1/23/660
= 1 × 660/23 = 660/23 days
= 28 16/23 days = or 28.696 days
Thus, Ronald and Jose working together will finish the work in 28 16/23 days = or 28.696 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 Ronald = 55 days
And the number of days required to finish the same work by Jose = 60 days
Thus, the number of days required to finish the work Ronald and Jose working together = ?
Here a = 55 days
And, b = 60 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Ronald and Jose working together
= 55 × 60/55 + 60 days
= 3300/115 days
= 3300 ÷ 5/115 ÷ 5 = 660/23 days
= 28 16/23 days or 28.696
Thus, Ronald and Jose together will finish the work in 28 16/23 days or 28.696 days Answer
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