A, B and C can do a work in 10, 12 and 15 days respectively. In how many days will the work be completed if B is assisted by both A and C on every third day?

8

A's one day work = 1/10

B's one day work = 1/12

C's one day work = 1/15

if b works for 2 consecutive days, work done = (1/12) + (1/12) = 2/12

if a and c assist b on the third day, total work done = (2/12) + 1/12 + 1/10 + 1/15 = (10+5+6+4)/60 = 25/60 = 5/12

if the same is repeated, upto 6th day work done = 2(25/60) = 10/12

now it is clearly observed that if B works alone for 2 more days the work done will be = 10/12 + 1/12 + 1/12 = 1

Total number of days taken as per the condition is 8 Days

The correct answer is Option (3) → 8