Question

A and B and can do a piece of work in 6 days B and C do it in 10 days and C and a do it in 15 days.
(a) in how many days will a b c finish it working together?
(b) in how many days will A and B finish a working alone?​

Answer 1

Solution :-

Given :
A and B and can do a piece of work in 6 days.
B and C do it in 10 days.
C and A do it in 15 days.


(A + B)'s one day work = 1/6
(B + C)'s one day work = 1/10
(C + A)'s one day work = 1/15


Find the (A + B + C)'s one day work :-

(A + B) + (B + C) + (C + A) = 1/6 + 1/10 + 1/15
=> 2(A + B + C) = (5 + 3 + 2)/30
=> A + B + C = 10/(30 × 2) = 1/6


A's one day work = (A + B + C) - ( B + C)
= 1/6 - 1/10
= (5 - 3)/30
= 2/30 = 1/15

B's one day work = (A + B + C) - (A + C)
= 1/6 - 1/15
= (5 - 2)/30
= 3/30 = 1/10

C's one day work = (A + B + C) - (A + B )
= 1/6 - 1/6
= (1 - 1)/6
= 0/6 = 0


Hence,
(a) A, B and C can do the work in 6 days.
(b) A and B finish the work alone in 15 days and 10 days respectively.