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6.	A vessel is filled with liquid, 3 parts of which are water and 5 parts of syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
	A.  1 / 3
	B.  1 / 4
	C.  1 / 5
	D.  1 / 7

Solution

Suppose the vessel initially contains 8 litres of liquid. Let x littres of this liquid be replaced with water. Quantity of water in new mixture = (3 - 3x/8 + x) litres. Quantity of syrup in new mixture = (5 - 5x/8) litres. (3 - 3x/8 + x) = (5 - 5x/8) = 5x + 24 = 40 - 5x =› 10x = 16 =› x = 8/5 So, part of the mixture replaced = (8/5 x 1/8) = 1/5.

7.	The cost of Type 1 rice is Rs.15 per kg and Type 2 rice is Rs.20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is
	A.  Rs.19.50
	B.  Rs.19
	C.  Rs.18
	D.  Rs.18.50

Solution

Let the price of the mixed variety be Rs. x per kg. By the rule of alligation, we have : Cost of 1 kg of type 1 rice Cost of 1 kg of type 2 rice (20-x)/(x-15) = 2/3 =› 60 - 3x = 2x - 30 =› 5x = 90 =› x = 18. so, price of the mixture is Rs. 18 per kg.

8.	In what ratio must water be mixed with milk costing Rs.12 per litre to obtain a mixture worth of Rs.8 per litre?
	A.  1 : 2
	B.  2 : 1
	C.  4 : 3
	D.  5 : 3

Solution

By the rule of alligation: C.P. of 1 litre of water C.P. of 1 litre of milk Ratio of water to milk = 4 : 8 = 1 : 2

9.	In what ratio must tea at Rs.62 per Kg be mixed with tea at Rs.72 per Kg so that the mixture must be worth Rs.64.50 per Kg?
	A.  3 : 1
	B.  3 : 2
	C.  4 : 3
	D.  5 : 3

Solution

By the rule of alligation: Cost of 1 kg tea of 1st kind Cost of 1 kg tea of 2nd kind Required ratio = 750 : 250 = 3 : 1

10.	Find the ratio in which rice at Rs.7.20 a kg be mixed with rice at Rs.5.70 a kg to produce a mixture worth Rs.6.30 a kg?
	A.  1 : 3
	B.  2 : 3
	C.  3 : 4
	D.  4 : 5

Solution

By the rule of alligation: Cost of 1 kg rice of 1st kind Cost of 1 kg rice of 2nd kind Required ratio = 60 : 90 = 2 : 3