Three pipes A, B and C can fill a tank in 8 hours. After working together for 2 hours B is closed and then A and C can fill in the remaining part in 8 hours. The number of hours taken by B alone to fill the cistern, is:

Question: Three pipes A, B and C can fill a tank in 8 hours. After working together for 2 hours, B is closed and then A and C can fill in the remaining part in 8 hours. The number of hours taken by B alone to fill the cistern, is:

Solution:
(A + B + C )'s 1 hour's work = 1/8 parts.

Part filled in 2 hours = 2/8 = 1/4 part.
Remaining part = 1- (1/4) = 3/4

Now,
(A + C)'s 8 hour's work = 3/4
∴ (A + C)'s 1 hour's work = 3/(4 × 8) = 3/32

∴ B's 1 hour's work = (1/8) - (3/32) parts [ এখানে (A + B + C ) - (A + C) বিয়োগ করে ]
= (4 - 3)/32
= 1/32 parts

1/32 parts work B can alone fill the tank in 1 hour
∴ 1 part work B can alone fill the tank in 1× (32/1) hours
= 32 hours

∴ B can alone fill the tank in 32 hours