Let
V = capacity of the tank
A,
B, and
C = rate of pipes
A,
B, and
C, respectively
Pipe A supplies 50 liters per minute more than B
$A = B + 50$
$A - B = 50$ ← Equation (1)
volume = rate × time
The Tank is initially empty and all pipes are opened (20 hours or 1200 minutes to fill):
$1200A + 1200B - 1200C = V$ ← Equation (2)
The tank is initially full and pipes A and C are opened (4 hours or 240 minutes to empty):
$V + 240A - 240C = 0$
$240A - 240C = -V$ ← Equation (3)
The tank is initially full and pipes B and C are opened (2 hours or 120 minutes to empty):
$V + 120B - 120C = 0$
$120B - 120C = -V$ ← Equation (4)
Equation (2) + Equation (3)
$1440A + 1200B - 1440C = 0$
$6A + 5B - 6C = 0$ ← Equation (5)
Equation (2) + Equation (4)
$1200A + 1320B - 1320C = 0$
$10A + 11B - 11C = 0$ ← Equation (6)
From Equations (1), (5), and (6)
$A = 110 ~ \text{Lit/min}$ ← [ C ] answer for part 1
$B = 60 ~ \text{Lit/min}$
$C = 160 ~ \text{Lit/min}$ ← [ B ] answer for part 2
From Equation (2)
$V = 1200(110) + 1200(60) - 1200(160)$
$V = 12,000 ~ \text{Lit}$ ← [ A ] answer for part 3
