Question:
If James can finish the work in 24 days and John can finish the same work in 40 days, then in how many days both can finish the work together?
Correct Answer
15 days
Solution And Explanation
Solution
Given,
The number of days to finish the work by James = 24 days
And, the number of days to finish the same work by John = 40 days
Thus, the number of days to finish the work by James and John together = ?
Here,
∵ In 24 days the work done by James = 1
∴ In 1 day, the work done by James = 1/24 part
Similarly,
∵ In 40 days the work done by John = 1
∴ In 1 day, the work done by John = 1/40 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
= 1/24 + 1/40
= 5 + 3/120
= 8/120 part of work
= 8 ÷ 8/120 ÷ 8 part of work
= 1/15 part of work
This means, in 1 day, 1/15 part of the work is done by James and John together.
Now, the number of days required to finish 1/15 part of work by James + John working together = 1
∴ the number of days required to finish 1 work by James + John together
= 1/1/15
= 1 × 15/1 = 15/1 days
= 15 days
Thus, James and John working together will finish the work in 15 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 = 24 days
And the number of days required to finish the same work by John = 40 days
Thus, the number of days required to finish the work James and John working together = ?
Here a = 24 days
And, b = 40 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when James and John working together
= 24 × 40/24 + 40 days
= 960/64 days
= 960 ÷ 64/64 ÷ 64 = 15/1 days
= 15 days
Thus, James and John together will finish the work in 15 days Answer
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