Question

Pipes A and B can fill a tank in 9 hours and 12 hours respectively. Both pipes are opened together to fill the tank but pipe B is closed after some time. If the tank is full in 6 hours, after how many hours was pipe B closed?​

Answer 1

||✪✪ GIVEN ✪✪||

• Pipe A can fill the tank alone in 9 hours.
• Pipe B can fill the tank alone in 12 hours.
• B is closed after some Time .
• The tank is full in 6 hours .

|| ✰✰ ANSWER ✰✰ ||

LCM of 9 and 12 = 36 units = Let Capacity of Tank.

So,

→ Efficiency of Tank A = (36/9) = 4 units/ hour.

→ Efficiency of Tank B = (36/12) = 3 units / hour.

Now, It has been said That, Tank B is closed after some Time. So, we can say That, Tank A work for all 6 hours.

So,

→ in 6 hours Tank A filled = 4 * 6 = 24 units.

_________________

→ Left to be filled now = 36 - 24 = 12 units.

So, This was Filled by B now , before closing .

→ 12 Units filled by B in = (12/3) = 4 hours.

Hence, We can say That, After 4 Hours Pipe B was Closed.

Answer 2

$\huge{\mathtt{Solution⇢}}$

$\mathtt{GIVEN⇢}$

$\mathtt{⇢\: Pipe \: A \: can \: fill \: the \: tank \: in \: 9 \: hours }$

$\mathtt{⇢\: Pipe\: B\: can\: fill\: in\: 12\: hours}$

$\mathtt{⇢\: Both\: pipes\: are\: opened\: together}$

$\mathtt{⇢\: Tank \: got \: filled \: in\: 6\: hours}$

______________________

$\mathtt{⇢\: Efficiency\: of \: pipes \: for \: filling\: tank \: per \: hour \: will :- }$

$\mathtt{⇢\: For \: this \: we'll\: find \: LCM }$

$\mathtt{⇢ \: LCM\: of \:9 \:and \:12\: is\: 36 }$

$\mathtt{⇢ \:Here \:36\: is\: the \:water \:holding \:capacity \:of \:the \:tank}$

$efficiency \: of \: a \: = \frac{36}{9} = 4$

$efficiency \: of \: b = \frac{36}{12} = 3$

$\mathtt{⇢ So \:pipe\: A \:is \:opened\: for\: complete\: 6 \: hours }$

$\mathtt{⇢\: A\: filled \:the\: portion\: of \:tank\: in \: 6 \: hours }$

$= 6 \times 4 = 24$

$\mathtt{⇢\:Here\: 4 \:is \:per \:hour \:filling \:efficiency\: of\: pipe\: A }$

$\mathtt{⇢\: So \:out\: of \:total \:capacity\: 24\: is \:filled \:by \:pipe\: A }$

$\mathtt{⇢\: Volume\: filled\: by\: pipe\: B\: =\: 36\:-\:24 \:=\: 12 }$

$\mathtt{⇢\: Per\: hour\: efficiency\: of\: pipe\: B \:=\: 3 }$

$time \: taken \: = \frac{12}{3} = 4hours$

${\mathtt{\red{⇢\: So \: pipe \:B\: is \:opened\: for\: 4 \:hours }}}$