A and B can finish the work in 20 days, while B and C can do it in 36 days. A started the work, worked for 5 days, then B worked for 10 days, and the remaining work was finished by C in 15 days. In how many days could C alone have completed the whole work?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 16.
A + B = 1 work ÷ 20 days = 9 units/day (taking total work = 180 units)
B + C = 1 work ÷ 36 days = 5 units/day
Sequence: A 5 days, B 10 days, C 15 days → total 180 units
Let B = y → A = 9 – y, C = 5 – y
Total work: 5A + 10B + 15C = 180 → 5(9–y) +10y +15(5–y) = 180
45 –5y +10y +75 –15y = 180 → –10y = 60 → y = –6
C = 5 – (–6) = 11 units/day
Total work ÷ C’s daily work = 180 ÷ 11 = 16 days