Question

P can complete a piece of work in 8 days, Q in 10 days and R in 12 days. Q and R together worked for 3 days, then R left the work and P replaced him. In how many days will the remaining work be completed?

a) 2 days b) 4 days c) 3 days d) 1 day e) 5 days

Answer 1

Answer:

Lcm of (12,16) = 48 units <--total work

So A+B = 48/12 = 4 units per day

B+C = 48/16 = 3 units per day

Now,

5A+7B+13C = 48 units

5 (A+B)+2 (B+C)+11C = 48

5 (4)+2 (3)+11C = 48

20+6+11C = 48

11C = 22

C = 2 units

So C does 2 units of work daily

So total time required to complete work alone is 48/2 = 24 days

I don't know why my answer is collapsing that's why I'm typing this useless things to prevent from collapsing