Pipes 1 and 2 can fill a tank in 18 and 24 hours respectively.

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Pipes 1 and 2 can fill a tank in 18 and 24 hours respectively. Both pipes work simultaneously for sometime after which Pipe 1 is
turned off. It takes 12 hours in all to fill the tank completely. Find the time for which Pipe 1 was turned on.

1. 9 hours
2. 10 hours
3. 11 hours
4. 12 hours

Correct Option: A

Let the time for which Pipe 1 is turned on be ‘t’ hours, hence Pipe 1 has worked for ‘t’ hours and Pipe 2 has worked for 12 hours.
According to question ,

∴	1	(t) +	1	(12) = 1
	18		24

⇒	t	+	1	= 1 or	t	=	1	⇒ t = 9
	18		2		18		2

∴ Pipe 1 was turned on for 9 hours.
Second method to solve this question :
For ‘t’ hours both pipes worked, and for (12 – t ) hours, only Pipe 2 worked, hence,

t		1	+	1		+	1	(12 - t) = 1
		18		24			24

	7	t -	t	=	1
	72		24		2

⇒	(14 - 6)t	=	1
	72 × 2		2

⇒ t =	1	×	2 × 72	= 9 hours
	2		8