Question

A B C together could do a piece of work in 60 days. They work
together for 10 days then A leaves off & B & C work together for20days
more, when B leaves off & C working1/3 longer each day, then finishes
alone in 96 more days. C working at his former rate, could have done
work alone in 222 days. How long would B alone take to complete the
168 days (b) 144 days (c) 120 days (d) 196 days​

Answer 1

Answer:

Let a, b, c be the three work rates

Working together, they can complete the job in 60 days:

a + b + c = 1 job/60 d = 1/60

After 10 days, the job is (1/60)*10 = 1/6 complete

B and C working together for 20 days complete this much of the job: 20(b+c)

Then C working alone completes the job in 96 days working 4/3 as much per day.

 

So C completes this much of the job: 96c(4/3) = 128c

C working alone can complete the job in 222 days, so c = 1/222

Since after the first 10 days 5/6 of the job gets completed, we can write:

5/6 = 128c + 20(b+c)

5/6 = 128/222 + 20b + 20/222

Simplifying gives 5/6 = 4/6 + 20b

b = (1/6)/20 = 1/120

So B can complete the job in 120 days

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