Alligation or Mixture

Q 1: Find the ratio in which rice at Rs. 8.10 a kg be mixed with rice at Rs. 7.10 a kg to produce a mixture worth Rs. 7.50 a kg. A)3 : 3 B)2 : 3 C)1 : 3 D)2 : 2 Answer : Option B Explanation: By the rule of Alligation: Cost of 1 kg of 1st kind 810 p and Cost of 1 kg of 2nd kind 710 p Mean price 750 p So, 810-750=60 and 750-710=40 Required ratio = 40 : 60 = 2 : 3. Q 2: The cost of Type 1 rice is Rs. 20 per kg and Type 2 rice is Rs. 25 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. 23 B)Rs. 33 C)Rs. 28 D)Rs. 22 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 rice Rs. 20 and Cost of 1 kg of Type 2 rice Rs.25 Mean price Rs. x So, 25-x and x-20 =>(25-x)/(x-20)=2/3 =>75-3x=2x-40 =>5x=115 =>x=115/5=23 x=Rs. 23 Q 3: How many kilogram of sugar costing Rs. 6 per kg must be mixed with 26 kg of sugar costing Rs. 8 per kg so that there may be a gain of 10% by selling the mixture at Rs. 8.24 per kg? A)82.8 kg B)58.9 C)65.5 D)72.8 kg Answer : Option D Explanation: S.P. of 1 kg of mixture = Rs. 8.24, Gain 10%. C.P. of 1 kg of mixture = Rs.(100/110)x 8.24=Rs.7.49 By the rule of allilation, we have: C.P. of 1 kg sugar of 1st kind Rs. 6 and C.P. of 1 kg sugar of 2nd kind Rs.8 and mean price Rs. 7.49 So, 6-7.49=1.49 and 8-7.49=0.51 Ratio of quantities of 1st and 2nd kind = 14 : 5 Let x kg of sugar of 1st be mixed with 26 kg of 2nd kind. Then 14:5=x:26 =>x=(14 x 26)/5=72.8 kg Q 4: 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)4/2 D)2/6 Answer : Option B Explanation: By the rule of alligation, we have: Strength of first jar 40% and Strength of second jar 19% and mean strength 26% So, 40-26=14 and 19-26=7 So, ratio of 1st and 2nd quantities = 7 : 14 = 1 : 2 Required quantity replaced =2/3
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Q 1: Find the ratio in which rice at Rs. 8.10 a kg be mixed with rice at Rs. 7.10 a kg to produce a mixture worth Rs. 7.50 a kg.

A)3 : 3
B)2 : 3
C)1 : 3
D)2 : 2

Answer : Option B

Explanation:
By the rule of Alligation:
Cost of 1 kg of 1st kind 810 p and Cost of 1 kg of 2nd kind 710 p
Mean price 750 p
So, 810-750=60 and 750-710=40
Required ratio = 40 : 60 = 2 : 3.

Q 2: The cost of Type 1 rice is Rs. 20 per kg and Type 2 rice is Rs. 25 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. 23
B)Rs. 33
C)Rs. 28
D)Rs. 22

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 rice Rs. 20 and Cost of 1 kg of Type 2 rice Rs.25
Mean price Rs. x
So, 25-x and x-20
=>(25-x)/(x-20)=2/3
=>75-3x=2x-40
=>5x=115
=>x=115/5=23
x=Rs. 23

Q 3: How many kilogram of sugar costing Rs. 6 per kg must be mixed with 26 kg of sugar costing Rs. 8 per kg so that there may be a gain of 10% by selling the mixture at Rs. 8.24 per kg?

A)82.8 kg
B)58.9
C)65.5
D)72.8 kg

Answer : Option D

Explanation:
S.P. of 1 kg of mixture = Rs. 8.24, Gain 10%.
C.P. of 1 kg of mixture = Rs.(100/110)x 8.24=Rs.7.49
By the rule of allilation, we have:
C.P. of 1 kg sugar of 1st kind Rs. 6 and C.P. of 1 kg sugar of 2nd kind Rs.8 and mean price Rs. 7.49
So, 6-7.49=1.49 and 8-7.49=0.51
Ratio of quantities of 1st and 2nd kind = 14 : 5
Let x kg of sugar of 1st be mixed with 26 kg of 2nd kind.
Then 14:5=x:26
=>x=(14 x 26)/5=72.8 kg

Q 4: 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)4/2
D)2/6

Answer : Option B

Explanation:
By the rule of alligation, we have:
Strength of first jar 40% and Strength of second jar 19% and mean strength 26%
So, 40-26=14 and 19-26=7
So, ratio of 1st and 2nd quantities = 7 : 14 = 1 : 2
Required quantity replaced =2/3

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