A and B can complete a work in 12 days, B and C in 15 days, and C and A in 20 days. In how many days will they complete the work a. together b. separately?
Answers
Answer:
answer is 27
Step-by-step explanation:
15 plus 12=27
Solution:
Time taken by A and B together (A+B) to complete the work = 12 days
Time taken by B and C together (B+C) to complete the word = 15 days
Time taken by C and A together (C+A) to complete the work = 20 days
=> (A+B) 's one - day work = 1/12
=> (B+C) 's one - day work = 1/15
=> (C+A)'s one - day work = 1/20
a. To find the time taken by A,B and C if they work together we add to get, (A+B) 's one - day work + (B+C) 's one - day
+ (C+A)'s one - day work = 2(A+B+C) 's one - day work.
=> 2(A+B+C) 's one - day work = 1/12 + 1/15 + 1/20
= 5+4+3/60 = 12/60 = 1/5
=> (A+B+C) 's one - day work = 1/10
Thus, A,B and C together (A+B+C) will complete the work in 10 days.
b. A's one - day work = (A+B+C) 's one - day work -(B+C) 's one - day work
= 1/10 - 1/15 = (3-2/30) = 1/30
Thus, A alone will complete the work in 30 days.
B's one - day work = (A+B+C)'s one - day work
-(A+B)'s one - day work
= 1/10 - 1/12 = (6-5/60) = 1/60
Hence, C alone will complete the work in 60 days