A and B can complete a task together in 12 days, while B and C can finish it in 16 days. After A works on it for 12 days and B for 8 days, C takes the remaining 8 days to finish the work. How many days would it take for C to complete the work alone?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 48 days
Work rate of A + B = 1/12
⇒ A = 1/12 - B .....(1)
Work rate of B + C = 1/16 .....(2)
Also, 12A + 8B + 8C = 1 .....(3)
Substitute A = 1/12 - B from (1) into (3):
12(1/12 - B) + 8B + 8C = 1
⇒ 1 - 12B + 8B + 8C = 1
⇒ 8C = 4B
⇒ C = B/2 .....(4)
Substitute C = B/2 into (2): B + B/2 = 1/16
⇒ (3B)/2 = 1/16
⇒ B = 1/24
⇒ C = B/2 = 1/48
Number of days C alone takes = 1/(1/48) = 48 days