Question

Two taps A and B fill a tank separately in 24 minutes and 40 minutes respectively and a waste pipe C releases 30 litres of water per minute. If all the pipes are opened the tank is filled in an hour. Find the capacity of the tank.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

$\underline{\underline{\huge{\textbf{Solution:}}}}$

Given,

$\underline{\textit{Statement-1:}}$
Two taps A and B fill a tank separately in 24 minutes and 40 minutes respectively

$\underline{\textit{Statement-2:}}$
Waste pipe C releases 30 litres of water per minute

$\underline{\textit{Statement-3:}}$
If all the pipes are opened the tank is filled in an Hour.

Capacity of the tank = ?

$\underline{\large{\textsf{Step-1:}}}$
Assume capacity of the tank as a Variable.

Let capacity of the tank be 'x' Litres

$\underline{\large{\textsf{Step-2:}}}$
Find the capacity of tank in 1 Hour
(As given in statement-3)

Capacity of tank = $\frac{x}{60}$————(1)

$\underline{\large{\textsf{Step-3:}}}$
Find the Part of the tank filled by pipes A and B in 1 minute

From statement -1,

Part of the tank filled by pipes A and B in 1 minute = $\frac{x}{24} + \frac{x}{40}$

$\underline{\large{\textsf{Step-4:}}}$
Find the Part of tank filled by A and B in one minute, when pipe C releases 30 lts of water per minute

Part of tank filled = $\frac{x}{24} + \frac{x}{40} - 30$————(2)

$\underline{\large{\textsf{Step-5:}}}$
Equate (1) & (2), as both specifies the capacity of the tank , referring to the same tank.

$\frac{x}{24} + \frac{x}{40} - 30 = \frac{x}{60}$

$\underline{\large{\textsf{Step-6:}}}$
Solve to obtain the value of the variable

$\implies \frac{x}{24} + \frac{x}{40} - \frac{x}{60} = 30$

$\implies \frac{10x+6x-4x}{240} = 30$

$\implies \frac{10x+2x}{240} = 30$

$\implies \frac{12x}{240} = 30$

$\implies \frac{x}{20} = 30$

$\implies x = 30 \times 20$

$\implies x = 600$

$\therefore$
$\star \textsf{The capacity of the tank is \underline{\textbf{600\: Litres}}}$