Riya and Sangeeta can finish a work in 6 days and 8 days, respectively. Riya started the work alone and then after 3 days, Sangeeta joined Riya. They both finish the remaining work. How long did the total work last?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. days.
Let's first find out how much work each of them can do in one day:
Riya can do 1/6th of the work in one day.
Sangeeta can do 1/8th of the work in one day.
In 3 days, Riya did 3 × (1/6) = 1/2 of the work.
So, the remaining work is 1 - 1/2 = 1/2.
Now, both of them work together to finish the remaining half of the work. In one day, they can do 1/6 + 1/8 = 7/24 of the work together.
To finish 1/2 of the work, they will take: (1/2) / (7/24) = 12/7 days.
So, the total time taken to finish the work is: 3 days (Riya alone) + 12/7 days (both together) = 33/7 days.
Therefore, the total work lasted 33/7 days.