Farhan can do a work in 6 days, while Uzair in 9 days. How many days will both take together to complete the work?
A. 2 days
B. 4 days
C. 5 days
D. 6 days
Explanation:
Let’s find out how much work Farhan and Uzair can do in one day individually.
Farhan can finish the work in 6 days, so his work rate per day is 1/6 (representing the fraction of work he completes each day).
Uzair can finish the work in 9 days, so his work rate per day is 1/9 (representing the fraction of work he completes each day).
Now, let’s calculate their combined work rate when they work together:
Combined work rate = Farhan’s work rate + Uzair’s work rate
Combined work rate = 1/6 + 1/9
To add these fractions, we find the common denominator, which is 18:
Combined work rate = (3/18) + (2/18)
Combined work rate = 5/18
To find out how many days it would take them to finish the work together, we divide 1 (the total work) by their combined work rate:
Time taken together = 1 / Combined work rate
Time taken together = 1 / (5/18)
Time taken together = 1 * (18/5)
Time taken together = 18/5 = 3.6
Now, we convert this improper fraction to a mixed fraction:
Time taken together = 3 3/5 days
Since we cannot have a fraction of a day, we round it up to the nearest whole day. So, both Farhan and Uzair will take 3.6≈4 days together to complete the work.
Therefore, the correct answer is B (4 days).