A,B and C can do one-third of a work in 15 days, 30 days and 10 days respectively. A started the work. C joined him after 1 day and B joined them after 3 days of the beginning. For how many days C work?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 15.
A’s 1 day work = 1/45
B’s 1 day work = 1/90
C’s 1 day work = 1/30
Lcm of 45,30,90 = 90 units
Efficiency of A = 90/45 = 2 units/day
Efficiency of B = 90/90 = 1 unit/day
Efficiency of C = 90/30 = 3 unit/day
Work done on 1st day = 2 units
Work done on 2nd and 3rd day = (3 + 2) × 2 = 10 units
Total work done till 3rd day = 10 + 2 = 12 units
Remaining = 90 - 12 = 78 units
Work done by A, B, and C in one day = 2 + 1 + 3 = 6 units
Days C will work = 78 ÷ 6 = 13 days
Total days C worked = 13 + 2 = 15 days.