Alligation or Mixture - General Questions

A merchant has 1000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is:

A.	400 kg
B.	560 kg
C.	600 kg
D.	640 kg

Answer: Option C

Explanation:

By the rule of alligation, we have:

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

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

Quantity of 2^nd kind =		3	x 1000	kg	= 600 kg.
		5

8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of water is 16 : 65. How much wine did the cask hold originally?

A.	18 litres
B.	24 litres
C.	32 litres
D.	42 litres

Answer: Option B

Explanation:

Let the quantity of the wine in the cask originally be x litres.

Then, quantity of wine left in cask after 4 operations =		x		1 -	8		4	litres.
					x

		x(1 - (8/x))⁴		=	16
		x			81

		1 -	8		4	=		2		4
			x					3

		x - 8		=	2
		x			3

3x - 24 = 2x

x = 24.

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. 18
B.	Rs. 18.50
C.	Rs. 19
D.	Rs. 19.50

Answer: Option A

Explanation:

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 riceCost 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.

In what ratio must a grocer mix two varieties of tea worth Rs. 60 a kg and Rs. 65 a kg so that by selling the mixture at Rs. 68.20 a kg he may gain 10%?

A.	3 : 2
B.	3 : 4
C.	3 : 5
D.	4 : 5

Answer: Option A

Explanation:

S.P. of 1 kg of the mixture = Rs. 68.20, Gain = 10%.

C.P. of 1 kg of the mixture = Rs.		100	x 68.20		= Rs. 62.
		110

By the rule of alligation, we have:

Cost of 1 kg tea of 1^st kind.Cost of 1 kg tea of 2^nd kind.
Rs. 60	Mean Price Rs. 62	Rs. 65
3		2

Required ratio = 3 : 2.

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

Answer: Option B

Explanation:

By the rule of alligation:

Cost of 1 kg of 1^st kindCost of 1 kg of 2^nd kind
720 p	Mean Price 630 p	570 p
60		90

Required ratio = 60 : 90 = 2 : 3.

In what ratio must water be mixed with milk to gain 16 1-div-2by3 % on selling the mixture at cost price?

A.	1 : 6
B.	6 : 1
C.	2 : 3
D.	4 : 3

Answer: Option A

Explanation:

Let C.P. of 1 litre milk be Re. 1.

S.P. of 1 litre of mixture = Re.1, Gain =	50	%.
	3

C.P. of 1 litre of mixture =		100 x	3	x 1		=	6
			350				7

By the rule of alligation, we have:

C.P. of 1 litre of waterC.P. of 1 litre of milk

Mean Price

Re.	6
	7

Re. 1

Ratio of water and milk =	1	:	6	= 1 : 6.
	7		7

A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containing 19% alcohol and now the percentage of alcohol was found to be 26%. The quantity of whisky replaced is:

A.	1/3
B.	2/3
C.	2/5
D.	3/5

Answer: Option B

Explanation:

By the rule of alligation, we have:

Strength of first jarStrength of 2^nd jar
40%	Mean Strength 26%	19%
7		14

So, ratio of 1^st and 2^nd quantities = 7 : 14 = 1 : 2

Required quantity replaced =	2
	3

A container contains 40 litres of milk. From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?

A.	26.34 litres
B.	27.36 litres
C.	28 litres
D.	29.16 litres

Answer: Option D

Explanation:

Amount of milk left after 3 operations =		40		1 -	4		3	litres
					40

=		40 x	9	x	9	x	9		= 29.16 litres.
			10		10		10

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