A, B, and C are three workers who can complete a certain piece of work. A alone can complete the work in 12 days. B alone can complete the same work in 3X days. B and C together can complete the work in X days. A and B start the work together and continue working for 4 days, after which they have to leave. If the remaining work is completed by C alone in 8 days, then find
X. 

A completes work in 12 days
B completes in 3X days
B + C together complete in X days
A and B work together for 4 days
C completes the remaining work in 8 days
We need to find the value of X. Work = Rate × Time, Let the total work (LCM of 12, 3X, X) = 24X A’s rate = 24X / 12 = 2X/day
B’s rate = 24X / 3X = 8 units/day
B + C rate = 24X / X = 24 units/day So, C’s rate = 24 − 8 = 16 units/day Work done by A and B in 4 days = (2X + 8) × 4 = 8X + 32 Remaining work = 24X − (8X + 32) = 16X − 32 C completes remaining work in 8 days → 8 × 16 = 128 So, 16X − 32 = 128
16X = 160
X = 10