Ram can do a piece of work in 12 days and Shyam can do the same work in 16 days. They both started work together, Ram left 2 days before the completion of work. Then the total work is completed in how many days?

Required Answer = [((16-2)  ×12 )/(12+16)  ] + 2 = (14 × 12)/28 + 2 = 8 days Alternate method: Ram  can do a job in 12 days & Shyam can do same job in 16 days.  Let assume total work =  LCM (12, 16) = 48 units So Ram can daily do = 48 / 12= 4 units & Shyam can do daily = 48/ 16  =  3 units So Ram left 2 days before the completion of work ,it means that Shyam worked alone in last 2 days Hence Shyam did in last 2 days = 3× 2 = 6 units So remaining work = 48 – 6 = 42 is done by both Hence they worked together initially for = 42/(4 + 3) = 42 / 7 =  6 days Hence total days for completing the work = 6 days + 2 days  =  8 days