A and B together can complete a piece of work in 25 days, B and C together can complete the same piece of work in 36 days, while C and A together can complete it in 30 days. If A, B, C, and D together can complete this piece of work in 18 days, then in how many days can D alone complete this piece of work?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 200
A and B can do a piece of work in 25 days
B and C can do the same work in 36 days
A and C can do the same work in 30 days
A, B, C and D together can complete this piece of work in 18 days.
Total days of work = Work/(One day work)
⇒ 1 day work of (A + B) = 1/25 ....(1
⇒ 1 day work of (B + C) = 1/36 ....(2
⇒ 1 day work of (A + C) = 1/30 ....(3
⇒ 1 day work of (A + B + C + D ) = 1/18 ....(4
Adding eq. (1, (2, and (3 -
⇒ 1 day work of 2(A + B + C) = 1/25 + 1/36 + 1/30 = (36 + 25 + 30)/900 = 91/900
⇒ 1 day work of (A + B + C) = 91/1800
⇒ 1 day work of D = 1 day work of (A + B + C + D) - 1 day work of (A + B + C) = 1/18 - 91/1800 = (100 - 91)/1800 = 9/1800 = 1/200
Total number of days in which work is completed by A = Work/(1 day work of A) = 1/(1/200) = 200 days