A and B can do a piece of work in 10 days, while B and C can do the same work in 15 days and C and A in 25 days. they started working together, after 4 days A left. After another 4 days B left. In how many days C can finish the remaining work?
Choose the correct answer
A) 16  B) 32  C) 64  D) 96  E) None of These
Let the rates of A, B and C be a, b, and c respectively.   A and B can do a piece of work in 10 days: a + b = 1/10;   B and C can do the same work in 15 days: b + c = 1/15;   C and A can do the same work in 25 days: c + a = 1/25.   Sum the above 3 equations: 2(a + b + c) = 31/150 --&gt; a + b + c = 31/300   Subtract a + b = 1/10 from above to get c = 1/300.   For 4 days all 3 worked and completed 4*(a + b + a) = 124/300 of the work.   For the next 4 days B and C worked and they completed 4(b + c) = 4/15 = 80/300 of the work.   So, by the time C is left alone 1 - (124/300 + 80/300) = 96/300 of the work is left to be completed by C alone.   Time = Job/Rate = (96/300)/(1/300)= 
<gadget id="calculator">(96/300)/(1/300)</gadget>
<output>96</output>
96 days.   Answer: 96
<result>D</result>
A and B can do a piece of work in 10 days, while B and C can do the same work in 15 days and C and A in 25 days. they started working together, after 4 days A left. After another 4 days B left. In how many days C can finish the remaining work?