Question 1

A milkman claims to sell milk at its cost price, still, he is making a profit of 30% since he has mixed some amount of water in the milk. What is the % of milk in the mixture?

Accepted Answer

Let the milk he bought is 1000 ml Let C.P of 1000 ml is Rs. 100 Here let he is mixing K ml of water He is getting 30% profit => Now, the selling price is also Rs. 100 for 1000 ml => 100 : K% = 100 : 30 10 : 3 is ratio of milk to water => Percentage of milk = 10 x 100/13 = 1000/13 = 76.92%

Question 2

A jar was full with honey. A person used to draw out 20% of the honey from the jar and replaced it with sugar solution. He has repeated the same process 4 times and thus there was only 512 gm of honey left in the jar, the rest part of the jar was fi…

Accepted Answer

Let the initial amount of honey in the jar was k, then 512 = k 1 - 1 5 4 o r 512 = k 4 5 4 => k = 512 × 625 256 => k = 1250 Hence initially the honey in the jar = 1.25 kg

Question 3

How many liters of oil at Rs. 40 per liter should be mixed with 240 liters of the second variety of oil at Rs.60 per liter so as to get a maximum whose cost is Rs.52 per liter?

Accepted Answer

Apply the Allegation Method and first calculate the ratio in which they have to be mixed. = 8 : 12 = 2 : 3 Thus, the two varieties of oil should be mixed in the ratio 2 : 3. So, if 240 liters of the second variety are taken, then 160 liters of the first variety should be taken.

Question 4

In a 40 litre mixture of alcohol & water, the ratio of alcohol and water is 5 : 3. If 20% of this mixture is taken out and the same amount of water is added then what will be the ratio of alcohol and water in final mixture?

Accepted Answer

Quantity of alohol in the mixture = 40 x 5/8 = 25 lit Quantity of water = 40 - 25 = 15 lit According to question, Required ratio = 20 - 40 x 20 100 x 5 8 15 - 40 x 20 100 x 3 8 + 40 x 20 100 = 20 15 - 3 + 8 = 1 : 1

Question 5

The amount of water (in ml) that should be added to reduce 9 ml lotion, containing 50% alcohol, to a lotion containing 30% alcohol is ?

Accepted Answer

Let us assume that the lotion has 50% alcohol and 50% water. ratio = 1:1 As the total solution is 9ml alcohol = water = 4.5ml Now if we want the quantity of alcohol = 30% The quantity of water = 70% The new ratio = 3:7 Let x ml of water be added We get, 4 . 5 4 . 5 + x = 3 7 => x=6 Hence 6ml of water is added.

Question 6

A mixture of 70 litres of Fruit Juice and water contains 10% water. How many litres of water should be added to the mixture so that the mixture contains 12.5% water ?

Accepted Answer

Quantity of fruit juice in the mixture = 70 - [70 x (10/100) ]= 63 litres. After adding water, juice would form 87.5% of the mixture. Hence, if quantity of mixture after adding x liters of water, [(87.5) /100 ]*x = 63 => x = 72 Hence 72 - 70 = 2 litres of water must be added.

Question 7

Milk and water are mixed in a vessel A as 4:1 and in vessel B as 3:2. For vessel C, if one takes equal quantities from A and B, find the ratio of milk to water in C.

Accepted Answer

Ratio of Milk and water in a vessel A is 4 : 1 Ratio of Milk and water in a vessel B is 3 : 2 Ratio of only milk in vessel A = 4 : 5 Ratio of only milk in vessel B = 3 : 5 Let 'x' be the quantity of milk in vessel C Now as equal quantities are taken out from both vessels A & B => 4/5 : 3/5 x 3/5-x x - 4/5 => 3 5 - x x - 4 5 = 1 1 (equal quantities) => x = 7/10 Therefore, quantity of milk in vessel C = 7 => Water quantity = 10 - 7 = 3 Hence the ratio of milk & water in vessel 3 is 7 : 3

Question 8

In what ratio should two varieties of sugar at Rs.18 per kg and Rs.24 Kg be mixed together to get a mixture whose cost is Rs.20 per kg?

Accepted Answer

4 : 2 = 2 : 1 Thus, the two varieties should be mixed in the ratio 2 : 1

Question 9

The concentration of glucose in three different mixtures (glucose and alcohol) is 12,35 and 45 respectively. If 2 litres, 3 litres and 1 litre are taken from these three different vessels and mixed. What is the ratio of glucose and alcohol in the ne…

Accepted Answer

Concentration of glucose are in the ratio = 1 2 : 3 5 : 4 5 Quantity of glucose taken from A = 1 liter out of 2 Quantity of glucose taken from B = 3/5 x 3 = 1.5 lit Quantity of glucose taken from C = 0.8 lit So, total quantity of glucose taken from A,B and C = 3.6 lit So, quantity of alcohol = (2 + 3 + 1) - 3.6 = 2.4 lit Ratio of glucose to alcohol = 3.6/2.4 = 3:2

Question 10

One type of liquid contains 25 % of benzene, the other contains 30% of benzene. A can is filled with 6 parts of the first liquid and 4 parts of the second liquid. Find the percentage of benzene in the new mixture.

Accepted Answer

Let the percentage of benzene = X (30 - X)/(X- 25) = 6/4 = 3/2 => 5X = 135 X = 27 So, required percentage of benzene = 27 %

Question 11

Equal quantities of three mixtures of milk and water are mixed in the ratio 1:2, 2:3 and 3:4. The ratio of water and milk in the mixture is ?

Accepted Answer

Given the three mixtures ratio as (1:2),(2:3),(3:4) (1+2),(2+3),(3+4) Total content = 3,5,7 Given equal quantities of the three mixtures are mixed, then LCM of 3, 5, 7 = 105 105/3 = 35 , 105/5 = 21 , 105/7 = 15 Now, the individual equal quantity ratios are (35x1, 35x2), (21x2, 21x3), (15x3, 15x4) i.e (35,70), (42,63), (45,60) So overall mixture ratio of milk and water is 35+42+45 : 70+63+60 122:193 But in the question asked the ratio of water to milk = 193 : 122

Question 12

The milk and water in two vessels A and B are in the ratio 4:3 and 2:3 respectively. In what ratio the liquids in both the vessels be mixed to obtain a new mixture in vessel c consisting half milk and half water?

Accepted Answer

Milk in 1-litre mixture of A = 4/7 litre. Milk in 1-litre mixture of B = 2/5 litre. Milk in 1-litre mixture of C = 1/2 litre. By rule of alligation we have required ratio X:Y X : Y 4/7 2/5 \ / (Mean ratio) (1/2) / \ (1/2 – 2/5) : (4/7 – 1/2) 1/10 1/1 4 So Required ratio = X : Y = 1/10 : 1/14 = 7:5

Question 13

An alloy of copper and bronze weight 50g. It contains 80% Copper. How much copper should be added to the alloy so that percentage of copper is increased to 90%?

Accepted Answer

Initial quantity of copper = 80 100 x 50 = 40 g And that of Bronze = 50 - 40 = 10 g Let 'p' gm of copper is added to the mixture => 50 + p x 90 100 = 40 + p => 45 + 0.9p = 40 + p => p = 50 g Hence, 50 gms of copper is added to the mixture, so that the copper is increased to 90%.

Question 14

In what ratio must wheat at Rs. 3.20/kg be mixed with wheat at Rs. 2.90/kg so that the mixture be worth Rs. 3/kg?

Accepted Answer

Given rate of wheat at cheap = Rs. 2.90/kg Rate of wheat at cost = Rs. 3.20/kg Mixture rate = Rs. 3/kg Ratio of mixture = 2.90 3.20 3 (3.20 - 3 = 0.20) (3 - 2.90 = 0.10) 0.20 : 0.10 = 2:1 Hence, wheat at Rs. 3.20/kg be mixed with wheat at Rs. 2.90/kg in the ratio of 2:1, so that the mixture be worth Rs. 3/kg.

Question 15

A milkman has 20 liters of milk. If he mixes 5 liters of water, which is freely available, in 20 liters of pure milk. If the cost of pure milk is Rs. 18 per litre, then the profit of the milkman, when he sells all the mixture at cost price, the prof…

Accepted Answer

As water costs free, water sold at cost price of milk gives the profit. Required profit % = 5/20 x 100 = 5 x 5 = 25%.

Question 16

There are two mixtures of honey and water in which the ratio of honey and water are as 1:3 and 3:1 respectively. Two litres are drawn from first mixture and 3 litres from second mixture, are mixed to form another mixture. What is the ratio of honey …

Accepted Answer

From the given data, The part of honey in the first mixture = 1/4 The part of honey in the second mixture = 3/4 Let the part of honey in the third mixture = x Then, 1/4 3/4 x (3/4)-x x-(1/4) Given from mixtures 1 & 2 the ratio of mixture taken out is 2 : 3 => 3 4 - x x - 1 4 = 2 3 => Solving we get the part of honey in the third mixture as 11/20 => the remaining part of the mixture is water = 9/20 Hence, the ratio of the mixture of honey and water in the third mixture is 11 : 9 .

Question 17

From a tank of petrol , which contains 200 liters of petrol, the seller replaces each time with kerosene when he sells 40 liters of petrol(or mixture). Everytime he sells out only 40 liters of petrol (pure or impure). After replacing the petrol with…

Accepted Answer

The amount of petrol left after 4 operations = 200 × 1 - 40 200 4 = 81.92 Hence the amount of kerosene = 200 - 81.92 = 118.08 liters

Question 18

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

Accepted Answer

Let he mixes the oils in the ratio = x : y Then, the cost price of the oils = 60x + 65y Given selling price = Rs. 68.20 => Selling price = 68.20(x+y) Given profit = 10% = SP - CP => 10/100 (60x + 65y) = 68.20(x+y)-(60x + 65y) => 6x + 6.5y = 8.20x + 3.20y =>2.2x = 3.3y => x : y = 3 : 2

Question 19

From the 50 liters of milk, 5 liters of milk is taken out and after it 5 liters of water is added to the rest amount of milk. Again 5 liters of milk and water is drawn out and it was replaced by 5 liters of water. If this process is continued simila…

Accepted Answer

General Formula: Final or reduced concentration = initial concentration x 1 - a m o u n t b e i n g r e p l a c e d i n e a c h o p e r a t i o n t o t a l a m o u n t n where n is the number of times the same operation is being repeated. The "amount being replaced" could be pure or mixture as per the case. similarly ,"total amount" could also be either pure or mixture. Here amount being replaced denotes the quantity which is to be withdrawn in each time. Therefore, 50 × 1 - 5 50 3 = 36.45 L

Question 20

In a mixture of 240 lt. water is 20% and rest is Milk. What quantity of mixture should be taken out and replaced with water so that water becomes 40%?

Accepted Answer

60 lit

Alligation or Mixture Questions