VMR Logics

ALLIGATIONS & MIXTURES

1. In what proportion one variety of oil 50 rupees per kg be mixed with another variety Rs. 100
per kg to get a mixture worth 80 rupee per kg

oil kg oil kg 

kg  
A) 2:3 B) 4:5 C) 1:2 D) 3:7
2. In what ratio must 25% alcohol be mixed with 50% alcohol to get a mixture of 40% alcohol
strength?

 

cs

A) 2:3 B) 3:2 C) 3:1 D) 1:3 E) None
3. A solution contians 25% Alcohol another solution contains certain % Alcohol. If these two
gi
soloutions are mixed in the ratio 2:3 then the resultant solution contains 40% Alcohol.


Lo

A) 30% B) 40% C) 50% D) 60%
4. One quality of wheat at Rs. 9.30 per kg mixed with another quality at a certain rate in the ratio
8:7. If the mixture so formed be worth Rs. 10 per kg. What is the rate per kg of the second
R

quality of wheat?

kgkg
M

kg 
A) Rs. 10.30 B) Rs. 10.60 C) Rs. 10.80 D) Rs. 11.00
V

5. A solution contains 25% Alcohol another solution contains 50% Alcohol of these two solutions
are mixed in the ratio 2:3 then the resultant solution contains – % Alcohol

   


A) 30% B) 40% C) 50% D) 60%
6. The cost of one type rice is Rs. 15 per kg and another type is Rs. 20 per kg. If these two
varieties rice are mixed in the ratio of 2:3 respectively then the price per kg of mixed variety of
rice is

   kg   kg 


A) Rs. 18.00 B) Rs. 18.50 C) Rs. 19.50 D) Rs. 19.00

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7. How much chicory at Rs. 4 per kg should be added to 15 kg of tea at Rs. 10 per kg so that the
mixture is worth Rs. 6.50 per kg?

kg kg kg


A) 20 kg B) 15 kg C) 21 kg D) 10 kg E) 25 kg

8. How many Kg of custard powder costing Rs. 40 a kg must be mixed with 16 kg of custard
powder costing Rs. 55 a kg so that 25% may be gained by selling the mixture at Rs. 60 a kg?

custard powder kg  custard powder kg kg

 kg  kg 


cs
A) 11 kg B) 14 kg C) 12 kg D)20 kg E) 15 kg
9. A mixture of 80 litres of wine and water contains 11% water. How many litres of water must be
added to make the water content 20% of the resulting mixture
gi
lit   

Lo
A) 5 B) 20 C) 7 D) 15
E) 10
10. A solution contains 10 litres mixture in which there is 10% Sulphuric acid. How much Sulphuric
acid is to be added to make the solution contains 25% Sulphuric acid?
R

lt
M


A) 2 lt B) 1 lt C) 4 lt D) 5 lt
V

E) Data inadequate
11. A chemical solution contains 30% water and 70% alkali. What quantity of water should be
added to 6 litres of solutions so that water content becomes 40% ?



A) 600 ml B) 1.2 litres C) 800 ml D) 1 litre E) None
12. 80 litre wine solution contains 90% water how much water must be removed to make the solu-
tion 50% water ?

litre

A) 16 lt B) 20 lt C) 11 lt D) 24 lt
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13. A solution of milk and water contains 70% milk, How much water should be added to 360
litres of the above solution so that the percentage of milk in the resultant solution becomes
60%?

 

A) 1440 litres B) 90 litres C) 240 litres D) 480 litres
E) None
14. The varieties of rice cost Rs. 10/kg, Rs. 20/kg and Rs. 30/kg. In what ratio should they be
mixed such that the mixture costs Rs. 23/kg

kg 
 kg

cs
15. Tea worth Rs. 126 per kg and Rs. 135 per kg is mixed with a third variety in the ratio 1:1:2. If
the mixture is worth Rs. 153 per kg, then the price of the third variety per kg will be

kg kg   

gi
kg 
A) Rs. 169.50 B) Rs. 170 C) Rs. 175.50 D) Rs. 180
Lo
16. In what proportion must rice at Rs. 15 per kg be mixed with rice at Rs. 18 per kg, So that the
mixture will be worth Rs. 16 per kg ?
kg kg 
kg 
R

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

17. A goldsmith has two qualities of gold one of 16 carats and another of 24 carats purity. In what
M

proportion should he mix both to make an ornament of 20 carats purity?

  
V

purity 
A) 2:1 B) 2:3 C) 3:1 D) 1:1
18. Gold and copper are 19 times and 9 times heavier than water respectively. An alloy of gold and
copper is prepared such that it is 15 times heavier than water. What is the proportion of gold
and copper?
 

A) 3:2 B) 2:3 C) 3:4 D) 4:3
19. How much water must be added to a cask which contains 40 litres of milk at cost price Rs. 3.5
per litre, so that the cost of milk reduces to Rs. 2 per litre?
 

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Alligations with Averages

20. A person has a chemical of Rs. 25 per litre. In what ratio should water be mixed in that
chemical so that after selling the mixture at Rs. 18 per litre he may get a profit of 20% ?
chemical chemical lit 

A) 3:2 B) 2:3 C) 3:5 D) 5:3
21. The average weight of two groups consisting of 45,75 people are 54 kgs, 65 kg then find the
average weight of all the people?
 

22. The average of 100 numbers is 44. if newly 4 numbers are join average of 104 numbers is 50.
then find the average of 4 new numbers?

cs
  

23. A cricketer whose bowling average is 24.85, runs per wicket,takes 5 wickets for 52 runs and
gi
thereby decreases his average by 0.85. The number of wickets taken by him till the last match
was:

Lo
 

A) 64 B) 72 C) 80 D) 96
24. The bowling average of a cricketer was 12.4.He improves his bowling average by 0.2 points
R

when he takes 5 wickets for 26 runs in his last match.The number of wickets taken by him
before the last match was:
M


  
V


A) 125 B) 150 C) 175 D) 200
25. The average expenditure of a boarding house is 150. if 8 boys left from the house the average
expenditure of the remaining increased by 10 rupee and the total expenditure decreased by
480. then find the number of students in the boarding house initially?

  

26. The Avg marks of 3 classes x, y, z is calculated. The average scores of x, y, z are 83, 76, 85.
The average score of xy is 79, y2 is 81 find the average score of all 3 classes?
x, y, z  
 x, y
y2 

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27. The average marks of 4 classes A, B, C, D is 60%. The individual average marks of classes are
respectively 45%, 50%, 92% and 80%. The average marks of AB is 48%, B in average marks
are 60%. Then find,
i) Average makrs % of A and D classes
ii) Also find students ratio of A and B

A, B, C, D 
 A, B,B,
CA, D 
 
A, D 

28. The average marks of entire class is A. The boys and girls were inthe ratio 3:1. The average
score of Boys is A+1 then find average score of girls is ?

cs
   A    
A+1 
29. gi
In an organization the average set of entire stall is 32000 and the average salary of officers is
68000, the average salary of non officers is 20,000. Then find the ratio of officers to non
officers. Also find how many officers are there, where total employees are 80
Lo
officers

officers officers 
R

Alligations with Ratio’s

M

30. In a place there are certain number of peacocks and rabbits are there. If the heads are counted
there are 90. while their legs are counted they are 224. find the number of peacocks?

 
V


31. In a purse there are certain number of 2 rupee, 5 rupee coins are there. Total number of coins
are 67 and total value in the purse is 260. find number of 2 rupee coins?



32. In an examination there are 40 questions are there, for each correct answer 4 marks will be
given and for each wrong answer 1 mark will be detected. Sandhya attempted all 40 questions
but she got only 10 marks. Find the ratio of correct answers to wrong answers?




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33. A solution contain acid and water in the ratio 7: 2. Another solution in the ratio 1:4. In what
ratio both the solutions are mixed so that the result should contain acid and water in the ratio
2:3?




34. A solution contain acid and water in the ratio 2: 5 another solution in the ratio 4:1. In what ratio
both the solutions are mixed so that the result should contain acid and water in the ratio 3 :2?





cs
35. A solution contain acid and water in the ratio 5: 2. Another solution in the ratio 7:6. In what
ratio both the solutions are mixed so that the result should contain acid and water in the ratio
8:5?
gi


Lo

36. A solution contains 80% copper and remaining Tin, and another solution contains 85% copper
and 12% tin. In what ratio both the solutions are mixed in order to obtain 15%. Tin in the reuslt
also find % copper in the result
R

Tin  Tin

 Tin, 
M


V

37. A solution contains 90% copper and remaining Tin, and another solution contains 93% copper
and 4% tin. In what ratio both the solutions are mixed in order to obtain 9%. Tin in the reuslt
also find % copper in the result

Tin  Tin

Tin, 


 kg 



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Alligations with %
39. A man bought 3 kg watermelon consisting 80% of water due to summer some of the water gets
evoparated now it contains 60% of water find the weight of watermelon


 

40. A man bought a watermelon which consisting 75% water. After few days due to summer it
reduced to 55% of water. At that time the weight of watermelon is 4kgs. Find initial weight.

 


cs

41. 40 lit of solution contains 14% salt. If 5 lit of water is evoperated now find the salt % ?

gi


42. In a village there are 20,000 people are there. In the next year males increased by 12% and
Lo
females increased by 10% and the total population becomes 22,100. Then find the number of
males?



R

A) 5000 B) 15000 C) 12000 D) 8000

M

43. In a village there are 20,000 people are there. In the next year males increased by 15% and
females decreased by 10% and the total population becomes 20,800. Then find the number of
males?
V




A) 5000 B) 15000 C) 12000 D) 8000

44. A solution of sugar syrup has 15% sugar. Another solution has 5% sugar. How many litres of
the second solution must be added to 20 litres of the first solution to make a solution of 10%
sugar?

sugar syrup sugar syrup  lit


A) 10 litres B) 5 litres C) 15 litres D) 20 litres

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Alligations with Profit & Loss

44. A man buys two horses for Rs.1350 and sells one so as to lose 6% and the other so as to gain
7.5% and on the whole he neither gains nor loses. What does first horse cost.


 
A) Rs. 750 B) Rs. 600 C) Rs. 700 D) Rs. 650
45. A trader has 120 kg of rice, out of which he sells some with 10% profit and the rest with 25%
profit. He gains 15% on the whole. What is the quantity of rice sold at 25% profit ?
kg rice 


cs
kg 
A) 30 kg B) 40 kg C) 50 kg D) 55 kg
46. gi
A man has 60 pens. He sells some of these at a profit of 12% and the rest at 8% loss. On the
whole, he gets a profit of 11%. How many pens were sold at 12% profit?

60 pens 

Lo
pens

A) 3 B) 57 C) 20 D) 40
47. A man has 40 kg of tea, a part of which he sells at 5% loss and the rest at the cost price. In this
R

business he gets a loss of 3%. Find the quantity which he sells at the cost price

kg
M

kg 
A) 16 kg B) 24 kg C) 25 kg D) 15 kg
V

48. If goods are purchased for Rs. 450 and 1/3rd part of the goods are sold at a loss of 10%, what
per cent of profit should be taken on the remainder so as to gain 20% on the whole transac-
tion?



A) 5% B) 65% C) 35% D) 30%
49. If goods are purchased for Rs. 840 and 1/4th part of the goods are sold at a loss of 25%, at
what gain per cent should the remainder be sold so as to gain 8% on the whole?



A) 21% B) 19% C) 24% D) 28%

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50. How many kg of tea at Rs. 42 per kg must a man mix with 25 kg of tea at Rs. 24 per kg so that
he may, on selling the mixture at Rs. 40 per kg. gain 25% on the outlay?
 kg  kg   kg 
kg 

A) 25 kg B) 32 kg C) 35 kg D) 20 kg
51. A man has Rs. 30000 rupees to lend on loan. He lent some of his capital to Mohan at an
interest rate of 20% per annum. At the end of one year he got 17% of his capital as interest.
How much did he lend to Mohan?




cs
A) Rs. 16250 B) Rs. 18000 C) Rs. 17000 D) Rs. 18750
52. Rs. 1500 is invested in two such parts that if one part be invested at 6%, and the other at 5%,
the total interest in one year from both investments is Rs. 85. How much is invested at 5% ?
gi
 

Lo

A) Rs. 1000 B) Rs. 800 C) Rs. 500 D) Rs. 700
53. Some amount of Rs. 7000 was lent at 6% p.a. and the remaining at 4% p.a. if the total simple
interest from both the fractions is 5 years was Rs. 1600, the sum lent at 6% p.a. was
R

 
  
M


A) Rs. 2000 B) Rs. 5000 C) Rs. 4000 D) Rs. 3000
V

Alligations with TD
54. A man travel 80 kms in 5 hrs partly by foot and partly by car on foot his speed was 8 km/hr and
on by car at 20 km/hr. Find the distance covered on foot ?
80 kms 
 20 kms 

55. A man travel 80 kms in 5 hrs partly by foot and partly by car on foot his speed was 8 km/hr and
on by car at 20 km/hr. Find the time taken on foot journey
80 kms 
 20 kms 

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56. Avinash covered 150 km distance in 10 hours. The first part of his journey he covered by car,
then he hired a rickshaw. The speed of car and rickshaw is 20 km/hr and 12 km/hr respec-
tively. The ratio of distances covered by car and the rickshaw respectively are:

 kms
km/hrkm/hr

A) 2 : 3 B) 4 : 5 C) 1 : 1 D) None of these
57. Two varieties of soda water with different prices is mixed in the ratio of 2 : 3. The price of first
soda water is Rs. 10 per litre while the price of second soda water is Rs. 15 per litre, respec-
tively. The average price of the mixture (per litre) is:


Rs.Rs.

cs

A) Rs. 12 B) Rs. 13 C) Rs. 14 D) Rs. 15
58. gi
A mixture of rice is sold at Rs. 3.00 per kg. This mixture is formed by mixing the rice of Rs.
2.10 and Rs. 2.52 per kg. What is the ratio of price of cheaper to the costlier quality in the
mixture if the profit of 25% is being earned.
Lo
  Rs.Rs.Rs.


A) 5 : 2 B) 2 : 7 C) 2 : 5 D) 15 : 8
R

59. Sharabi Chand purchased two different kinds of alcohol. In the first mixture the ratio of alcohol
to water is 3 : 4 and in the second mixture it is 5 : 6. If he mixes the two given mixtures and
M

makes a third mixture of 18 litres in which the ratio of alcohol to water is 4 : 5 the quantity of
first mixture (whose ratio is 3 : 4) is required to make the 18 litre of the third kind of mixture is:
V





A) 6 B) 7 C) 8 D) 9
60. Some amount out of Rs. 6000 was lent out at 10% per annum and the rest amount @ at 20%
per annum and thus in 4 years the total interest from both the amounts collected was Rs. 3400.
What is the amount which was lent out @ 10% per annum?

Rs.
 Rs. 

A) Rs. 2500 B) Rs. 2800 C) Rs. 3200 D) Rs. 3500
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61. In a municipal parking there are some two wheelers and rest are 4 wheelers. If wheels are
counted, there are total 520 wheels but the incharge of the parking told me that there are only
175 vehicles. If no vehicle has a stepney, then the no. of two wheelers is:


    

A) 75 B) 100 C) 90 D) 85

62. Modern electronic shop sold the 30% hardware at the profit of 50% and 90% software at the
profit of 10%. The average profit percent of the Modern electronic shop is, if it sells only these
two kinds of things:



cs


A) 15 B) 20 C) 25 D) 45

63.
gi
A milkman has two types of milk. In the first container the percentage of milk is 80% and in the
second container the percentage of milk is 60%. If he mixes 28 litres of milk of the first con-
tainer to the 32 litres of milk of the second container, then the percentage of milk in the mixture
Lo
is:




R

A) 63.99 B) 69.33 C) 72.5 D) 75.2

M

64. Mitthu Bhai sells rasgulla (a favorite Indian sweets) at Rs. 15 per kg. A rasgulla is madeup of
flour and sugar in the ratio of 5:3. The ratio of price of sugar and flour is 7:3 (per kg). Thus he
V

2
earns 66 % profit. What is the cost price of sugar?
3

Rs    


2
66 % 
3

A) Rs. 10/kg B) Rs. 9/kg C) Rs. 18/kg D) Rs. 14/kg

65. There are two alloys made up of copper and aluminium. In the first alloy copper is half of the
aluminium and in the second alloy copper is thrice as much as aluminium. How many times the
second alloy must be mixed with first alloy to get the new alloy in which copper is twice as that
of aluminium?
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 

  

A) 2 B) 3 C) 4 D) 5
66. The ratio of copper and nickel by weight in the two alloys X and Y are 2 : 7 and 5 : 4. How
many kilogram of the alloy X and Y are required to make 42 kg of new alloy Z in which the
ratio of copper and nickel is same?
XY
XYZZ

A) 6 kg and 36 kg B) 10 kg and 32 kg C) 7 kg and 35 kg D) none of these

cs
67. Two liquids are mixed in the ratio 4 : 3 and the mixture is sold at Rs. 20 with a profit of

1
33 % . If the first liquid is costlier than the second by Rs. 7. Find the sum of costs of both the
3
liquids:
gi
Lo
1
 33 %
3
 

R

A) Rs. 11 B) Rs. 29 C) Rs. 35 D) Rs. 70

68. Mrs. Annapurna per day sells exactly four quintal sugar at Rs. 2000 per quintal getting the
M

profit of Rs. 25%. Since she mixes two varieties of sugar, one costs Rs. 14 per kg and another
costs Rs. 22 per kg. One day due to huge demand in markets she had only 3 qunital of the
required mixture so she purchased the sugar costs Rs. 17 per kg at Rs. 18 per kg from the
V

wholeseller on that day and then she mixed 300 kg mixture with 100 kg sugar costing Rs. 18
per kg to fullfill the demand of the market selling at the same price. How much percent less
does she gain that she would have gained, if she had sufficient quantity of usual mixture of
sugar?



demand  
whole seller

  demand 

A) 12.5% B) 18.18% C) 62.5% D) Can’t determined
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69. A tin contains a mixture of Dew and Sprite in the ratio of 7 : 3 and another tin contains the Dew
and Sprite in the ratio of 5 : 4. In what proportion should the solution of two tins be mixed to
achieve a perfect proportion of 2 : 1 (in which Dew is 2 times that of sprite).
Mountain dewSprite

Mountain dewSprite
A) 10 : 3 B) 4 : 1 C) 3 : 10 D) 3 : 1
70. Michel travelled from New York to New Jersey covering total distance of 250 miles in 8 hr.
partly by car at 30 miles / hr. and rest by train at 35 miles / hr. The distance travelled by car is:
miles 



cs
A) 150 miles B) 80 miles C) 220 miles D) 180 miles
71. A goldsmith has 361 rings of gold. He sells some of them at a loss of 4% and rest at a profit of
15% making overall profit of 8%. Find the no. of rings sold at a profit of 15%.
gi
    
 

Lo
A) 171 B) 133 C) 218 D) 228
72. A girl buys 2 pigeons for Rs. 182. She sells one at a loss of 5% and another at a profit if 8%.
But she neither gains nor loses on the whole. Find the price of pigeon which has sold at a profit:

R



M

A) Rs. 112 B) Rs. 85 C) Rs. 70 D) can’t be determined

73. Petrol is 7 times heavy than Kerosene and Castrol mobil is 18 times as heavy as Kerosene.
What should be the ratio of petrol and mobil in the new mixture to get the mixture which must
V

be 11 times as heavy as kerosene?

Castrol mobil
Castrol mobil

A) 3 : 4 B) 7 : 4 C) 9 : 19 D) 9 : 10
74. A and B are two alloys of copper and tin prepared by mixing the respective metals in the ratio
of 5 : 3 and 5 : 11 respectively. If the alloys A and B are mixed to form a third alloy C with an
equal proportion of copper and tin, what is the ratio of alloys A and B in the new alloy C ?
ABA
BC 
CAB
A) 3:5 B) 4:5 C) 3:2 D) 2:3
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75. There are two vessels containing the mixture of milk and water. In the first vessel th e water is
2 / 3 of the milk and in the second vessel water is just 40% of the milk. In what ratio these are
required to mix to make 24 litres mixture in which the ratio of water is to milk is 1 : 2?


 

A) 4 : 3 B) 5 : 7 C) 5 : 2 D) 7 : 5
76. The ratio of expenditure and savings is 3 : 2. If the income increases by 15% and the savings
increases by 6%, then by how much percent should his expenditure increases?



cs
A) 25 B) 21 C) 12 D) 24
77. The average weight of boys in a class is 30 kg and the average weight of girls in the same class
gi
is 20 kg. If the average weight of the whole class is 23.25 kg, what would be the possible
strength of boys and girls respectively in the same class?
 
Lo
 

A) 14 and 26 B) 13 and 27 C) 17 and 27 D) none of these
78. The average marks of the students in four sections A, B, C and D together is 60%. The average
R

marks of the students of A, B, C and D individually are 45%, 50%, 72% and 80% respec-
tively. If the average marks of the students of sections A and B together is 48% and that of the
M

students of B and C together is 60%. What is the ratio of number of students in sections A and
D?
A,B,CD  
V

A,B,CD 
A B  B C
AD   
A) 2 : 3 B) 4 : 3 C) 5 : 3 D) 3 : 5
79. The ratio of water and alcohol in two different containers is 2 : 3 and 4 : 5. In what ratio we are
required to mix the mixtures of two containers in order to get the new mixture in which the ratio
of alcohol and water be 7 : 5?



A) 7 : 3 B) 5 : 3 C) 8 : 5 D) 2 : 7

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80. The average age of boys in class is 16.66, while the average age of girls is 18.75. Thus the
average age of all the 40 students of the class is 17.5. If the difference between the no. of boys
and girls is 8, then the no. of girls in the class is:



A) 12 B) 16 C) 18 D) data insufficient

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