Question : If A can finish a work in 10 days and B can finish the same work in 15 days, then in how many days they both can finish the work working together?
Correct Answer 6 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by A = 10 days
And, the number of days to finish the same work by B = 15 days
Thus, the number of days to finish the work by A and B working together = ?
Here, ∵ In 10 days the work done by A = 1
∴ In 1 day, the work done by A = 1/10
Similarly, ∵ In 15 days the work done by B = 1
∴ In 1 day, the work done by B = 1/15
Now, in 1 day, the work done by A and B together
= In 1 day work done by A + In 1 day the work done by B
= 1/10 + 1/15
= 3 + 2/30
= 5/30 6
= 1/6
This means in 1 day, 1/6 part of work is done by A and B working together.
Now, the number of days required to finish 1/6 work by A + B working together = 1
∴ the number of days required to finish 1 work by A + B working together
= 1/1/6
= 1 × 6/1 days= 6 days
Thus, A and B working together will finish the work in 6 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 to finish the work by A = 10 days
And, the number of days to finish the same work by B = 15 days
Thus, the number of days to finish the work by A and B working together = ?
Here "a" = 10 days
And, "b" = 15 days
Thus, using formula a × b/a + b days
The number of days reqire to finish the work when they work together
= 10 × 15/10 + 15
= 150/25 = 6
Thus, while working A and B together the number of days require to finish the work = 6 days Answer
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