A, B and C can do a piece of work in 20, 30 and 50 days, respectively. In how many days can A do the work, if he is assisted by B and C on every second day?
Show answer & explanation
Correct answer: A
Explanation
LCM of 20, 30, 50 = 300
Total Work = 300 units
A's Rate = 300 ÷ 20 = 15
B's Rate = 300 ÷ 30 = 10
C's Rate = 300 ÷ 50 = 6
Work on Day 1 (A only) = 15
Work on Day 2 (A + B + C) = 15 + 10 + 6 = 31
Work in 2 days = 15 + 31 = 46
Work in 12 days (6 cycles) = 46 x 6 = 276
Remaining Work = 300 − 276 = 24
Day 13 (A only) = 276 + 15 = 291
Remaining = 300 − 291 = 9
Day 14 (A + B + C)
Time required for 9 units = 9 ÷ 31 days
Total Time = 13 + (9 ÷ 31) = 13 days