One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:

Part filled by (A + B) in 1 minute =	❨	1	+	1	❩	=	1	.
		60		40			24

Suppose the tank is filled in x minutes.

Then,	x	❨	1	+	1	❩	= 1
	2		24		40

⟹	x	x	1	= 1
	2		15

⟹ x = 30 min.

Part filled in 4 minutes = 4	❨	1	+	1	❩	=	7	.
		15		20			15

Remaining part =	❨	1 -	7	❩	=	8	.
			15			15

Part filled by B in 1 minute =	1
	20

∴	1	:	8	:: 1 : x
	20		15

x =	❨	8	x 1 x 20	❩	= 10	2	min = 10 min. 40 sec.
		15				3

∴ The tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec.

Work done by the leak in 1 hour =	❨	1	-	3	❩	=	1	.
		2		7			14

∴ Leak will empty the tank in 14 hrs.

Net part filled in 1 hour	❨	1	+	1	-	1	❩	=	17	.
		5		6		12			60

∴ The tank will be full in	60	hours i.e., 3	9	hours.
	17		17

Time taken by one tap to fill half of the tank = 3 hrs.

Part filled by the four taps in 1 hour =	❨	4 x	1	❩	=	2	.
			6			3

Remaining part =	❨	1 -	1	❩	=	1	.
			2			2

∴	2	:	1	:: 1 : x
	3		2

⟹ x =	❨	1	x 1 x	3	❩	=	3	hours i.e., 45 mins.
		2		2			4

So, total time taken = 3 hrs. 45 mins.

By the rule of alligation, we have:

Profit on 1st part Profit on 2nd part
8%	Mean Profit 14%	18%
4		6

Ration of 1^st and 2^nd parts = 4 : 6 = 2 : 3

∴ Quantity of 2nd kind =	❨	3	x 1000	❩kg	= 600 kg.
		5

Let the price of the mixed variety be Rs. x per kg.

By rule of alligation, we have:

Cost of 1 kg of Type 1 rice Cost of 1 kg of Type 2 rice
Rs. 15	Mean Price Rs. x	Rs. 20
(20 - x)		(x - 15)

∴	(20 - x)	=	2
	(x - 15)		3

⟹ 60 - 3x = 2x - 30

⟹ 5x = 90

⟹ x = 18.

Let the cost of 1 litre milk be Re. 1

Milk in 1 litre mix. in 1st can =	3	litre, C.P. of 1 litre mix. in 1st can Re.	3
	4		4

Milk in 1 litre mix. in 2nd can =	1	litre, C.P. of 1 litre mix. in 2nd can Re.	1
	2		2

Milk in 1 litre of final mix. =	5	litre, Mean price = Re.	5
	8		8

By the rule of alligation, we have:

C.P. of 1 litre mixture in 1st can    C.P. of 1 litre mixture in 2nd can
3 4	Mean Price 5 8	1 2
1 8		1 8

∴ Ratio of two mixtures =	1	:	1	= 1 : 1.
	8		8

So, quantity of mixture taken from each can =	❨	1	x 12	❩	= 6 litres.
		2

By the rule of alligation:

Cost of 1 kg pulses of 1st kind Cost of 1 kg pulses of 2nd kind
Rs. 15	Mean Price Rs. 16.50	Rs. 20
3.50		1.50

∴ Required rate = 3.50 : 1.50 = 7 : 3.

Since first and second varieties are mixed in equal proportions.

So, their average price = Rs.	❨	126 + 135	❩	= Rs. 130.50
		2

So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.

By the rule of alligation, we have:

Cost of 1 kg of 1st kind Cost of 1 kg tea of 2nd kind
Rs. 130.50	Mean Price Rs. 153	Rs. x
(x - 153)		22.50

∴	x - 153	= 1
	22.50

⟹ x - 153 = 22.50

⟹ x = 175.50