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Home > Arithmetic Aptitude > Alligation or Mixture > Questions and Answers

Exercise:

Exercise 1

► Exercise 2

01. A tank of 100 litres is filled with kerosene. Ram replaces 10% of kerosene with water and repeats this procedure 4 times. What is the amount of kerosene left in the tank?
A. 60 litres B. 65.61 litres
C. 70 litres D. 65 litres

Answer and Explanation

Answer: 65.61 litres

Explanation:
As Ram replaces 10% of kerosene with water, the amount of kerosene left is 90%.
As the replacement is done four times,
After 1st replacement, kerosene left is : 0.9*100 = 90 litres
After 2nd replacement, kerosene left is : 0.9*90 = 81 litres
After 3rd replacement, kerosene left is : 0.9*81 = 72.9 litres
After 4th replacement, kerosene left is : 0.9*72.9 = 65.61 litres

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02. 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 and Explanation

Answer: 3 : 2

Explanation:

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03. Two liquids are mixed in the ratio 5:3 and by selling the mixture at Rs 12.25 / liter, a profit of 16 2/3 percent is made. If the first liquid costs Rs 4 / liter more than the second, find the price per liter of each liquid.
A. Rs 4 and Rs 12 B. Rs 8 and Rs 12
C. Rs 12 and Rs 8 D. Rs 8 and Rs 9

Answer and Explanation

Answer: Rs 8 and Rs 12

Explanation:
SP of mixture = 12.25
CP of mixture = 12.25(100/116 2/3) = 10.50
Let the CP of the two liquids be Rs x and Rs x+4 respectively

Price liquid1=x+4, liquid2=x
Resultant = 10.5

Proportion 10.5-x : x-6.5

(10.5 - x)/(x – 6.5) = 5/3 =>x=8
Prices of the two liquids = Rs 8 and Rs 12

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04. A cup of milk contains 3 parts of pure milk and 1 part of water. How much of the mixture must be withdrawn and water substituted in order that the resulting mixture may be half milk and half water?
A. ½ part B. 1/3 part
C. ¼ part D. ¾ part

Answer and Explanation

Answer: 1/3 part

Explanation:
The mixture contains ¾ part milk and ¼ part water
Let quantity of mixture withdrawn be x
Quantity of milk in the new mixture = ¾ - 3x/4
Quantity of water in the new mixture = ¼ - x/4 + x
¾ - 3x/4 = ¼ - x/4 + x =>x=1/3
1/3 part of the mixture should be withdrawn

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05. A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25%. The percentage of water in the mixture is:
A. 4% B. 6 %
C. 20% D. 25%

Answer and Explanation

Answer: 20%

Explanation:

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06. Three equal glassed are filled with mixtures of spirit and water. The proportion of spirit to water in each glass is as follows: in the first glass as 2:3, in the second glass as 3:4 and in the third glass as 4:5. The content of the three are emptied into a single vessel. What is the proportion of spirit and water?
A. 401 : 544 B. 300 : 544
C. 412 : 544 D. 232:300

Answer and Explanation

Answer: 401 : 544

Explanation:
Let the volumes of all the glasses be 10 liters
Glass1 Spirit= 4 ,Water = 6, Total= 10
Glass2 Spirit= 30/7 ,Water = 40/7, Total= 10
Glass3 Spirit= 40/9 ,Water = 50/9, Total= 10

Mixture Spirit= 802/63 ,Water = 1088/63, Total= 30

Spirit : Water = 803 : 1088 = 401 : 544

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07. How many kilograms of sugar costing Rs. 8 per kg must be mixed with 252 kg of sugar costing Rs. 4.5 per kg so that a profit of 10% maybe made by selling the mixture at Rs. 6.6 per kg?
A. 188kg B. 189kg
C. 198kg D. 187 kg

Answer and Explanation

Answer: 189kg

Explanation:
S.P = Rs. 6.6/kg.
SP = 110 CP / 100 => CP = (6.6 * 100)/110 = Rs. 6 = Mean Price
Rs. 4.50 / kg                                     Rs. 8 / kg
                              
                                  [6]

(8-6)                                                  (6 – 4.5)
Rs. 2 / kg                                          Rs. 1.50 / kg

Quantity of dearer / Quantity of cheaper = 1.5/2
Quantity of dearer = 252 x 1.5/2 = 126 x 1.5 = 189 kg.

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08. One alloy of metal contains 90% copper and 10% tin. Another contains 93% copper and 4% tin. If they are mixed so that the mixture may contain 9% of tin, what percent of copper will it contains?
A. 90.5% B. 81.33%
C. 77% D. 98%

Answer and Explanation

Answer: 90.5%

Explanation:
Quantity of Tin Alloy1=10 and Alloy2=4
Quantity of Mixture 9
Proportion 5:1
The two alloys should be mixed in the ratio 5:1
Amount of copper in the mixture = 5(90/100)+1(93/100) = 5.43
% of copper in the mixture = [5.43/(5+1)]100= 90.5%

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09. In what ratio must a grocer mix two varieties of food grains costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?
A. 3 : 7 B. 5 : 7
C. 7 : 3 D. 7 : 5

Answer and Explanation

Answer: 7 : 3

Explanation:
By the rule of alligation:
Cost of 1 kg food grain of 1st kind Cost of 1 kg food grain of 2nd kind

Rs. 15                         Mean Price                   Rs. 20
3.50                             Rs. 16.50                      1.50

Required rate = 3.50 : 1.50 = 7 : 3

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10. One alloy contains silver and copper in the ratio of 5:1 and the other contains them in the ratio of 7:2 respectively. What weights of the two must be melted together, so as to make a 5 lb mass with 80% silver?
A. 1/0.9 B. 2/3.5
C. 1/2 D. 2/3

Answer and Explanation

Answer: 2/3

Explanation:
Alloy1 silver=5,Copper = 1
Alloy2 silver=7,Copper = 2

Quantity of silver in alloy1=5/6
Quantity of silver in alloy2=7/9


Quantity of silver in Mixture=80/100=4/5

Proportion 1/45 : 1/30
The two alloys should be mixed in the ratio (1/45)/(1/30) = 2/3

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