Question : If James can finish the work in 2 days and John can finish the same work in 5 days, then in how many days both can finish the work together?
Correct Answer 1 3/7 days or 1.429 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by James = 2 days
And, the number of days to finish the same work by John = 5 days
Thus, the number of days to finish the work by James and John together = ?
Here,
∵ In 2 days the work done by James = 1
∴ In 1 day, the work done by James = 1/2 part
Similarly,
∵ In 5 days the work done by John = 1
∴ In 1 day, the work done by John = 1/5 part
Now, in 1 day, the work done by James and John together
= In 1 day work done by James + In 1 day the work done by John
= 1/2 + 1/5
= 5 + 2/10
= 7/10 part of work
This means in 1 day, 7/10 part of work is done by James and John working together.
Now, the number of days required to finish 7/10 part of work by James + John working together = 1
∴ the number of days required to finish 1 work by James + John together
= 1/7/10
= 1 × 10/7 = 10/7 days
= 1 3/7 days = or 1.429 days
Thus, James and John working together will finish the work in 1 3/7 days = or 1.429 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 James = 2 days
And the number of days required to finish the same work by John = 5 days
Thus, the number of days required to finish the work James and John working together = ?
Here a = 2 days
And, b = 5 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when James and John working together
= 2 × 5/2 + 5 days
= 10/7 days
= 1 3/7 days or 1.429
Thus, James and John together will finish the work in 1 3/7 days or 1.429 days Answer
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