Question

Working alone Trisha can complete a job in 80 minutes. Mona can complete the same job in two hours. They worked together for 30 minutes when Nanda, their friend, joined and for helping them. They finished the job 10 minutes later. How long would it take Nanda to complete the total alone.

Answer 1

Nanda would take 60 minutes to complete the job alone.

Explanation:

Let's say the amount of work required to finish the job is 'x'

If we call the speed of Trisha "T", of Mona "M" and of Nanda "N", we have that:

x = T * 80 -> T = x/80

x = M * 120 -> M = x/120

If Trisha and Mona worked together for 30 minutes, we can write that the amount of work completed is:

(T + M) * 30

Then, they 3 completed the work after 10 minutes, so we have that:

(T + M) * 30 + (T + M + N) * 10 = x

30T + 30M + 10T + 10M + 10N = x

40T + 40M + 10N = x

Replacing T by x/80 and M by x/120, we have:

40x/80 + 40x/120 + 10N = x

x/2 + x/3 + 10N = x

10N = x - x/2 - x/3

10N = (6x - 3x - 2x)/6

10N = x/6

N = x/60 -> x = N * 60

So Nanda would take 60 minutes to complete the job alone.