Question 1

A milk man sells the milk at the cost price but he mixes the water in it and thus he gains 9.09%. The quantity of water in the mixture of 1 liter is :

Accepted Answer

Profit (%) = 9.09 % = 1/11 Since the ratio of water and milk is 1 : 11, Therefore the ratio of water is to mixture = 1:12 Thus the quantity of water in mixture of 1 liter = 1000 x (1/12) = 83.33 ml

Question 2

The average weight of boys in a class is 30 kg and the average weight of girls in the same class is 20kg. If the average weight of the whole class is 23.25 kg, what could be the possible strength of boys and girls respectively in the same class?

Accepted Answer

13 and 27

Question 3

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.

Accepted Answer

2:3

Question 4

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?

Accepted Answer

5:3

Question 5

In the 75 litres of mixture of milk and water, the ratio of milk and water is 4:1. The quantity of water required to make the ratio of milk and water 3:1 is

Accepted Answer

5 litres

Question 6

From a container, 6 liters milk was drawn out and was replaced by water. Again 6 liters of mixture was drawn out and was replaced by the water. Thus the quantity of milk and water in the container after these two operations is 9:16. The quantity of …

Accepted Answer

Let quantity of mixture be x liters. Suppose a container contains x units of liquid from which y units are taken out and replaced by Water. After operations , the quantity of pure liquid = x 1 - y x n units, Where n = no of operations . So, Quantity of Milk = x 1 - 6 x 2 Given that, Milk : Water = 9 : 16 => Milk : (Milk + Water) = 9 : (9+16) => Milk : Mixture = 9 : 25 Therefore, x 1 - 6 x 2 x = 9 25 => x = 15 liters

Question 7

In a pot, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk, the pot would be full and ratio of milk and water would become 6 : 5. Find the capacity of the pot ?

Accepted Answer

Let the capacity of the pot be 'P' litres. Quantity of milk in the mixture before adding milk = 4/9 (P - 8) After adding milk, quantity of milk in the mixture = 6/11 P. 6P/11 - 8 = 4/9(P - 8) 10P = 792 - 352 => P = 44. The capacity of the pot is 44 liters.

Question 8

In a mixture of milk and water, there is only 26% water. After replacing the mixture with 7 liters of pure milk , the percentage of milk in the mixture become 76%. The quantity of mixture is:

Accepted Answer

Milk Water 74% 26% (initially) 76% 24% ( after replacement) Left amount = Initial amount 1 - r e p l a c e d a m o u n t t o t a l a m o u n t 24 = 26 1 - 7 k => k = 91

Question 9

Ratio of water and milk in a container is 2 : 3. If 40 liter mixture removed from the container and same quantity of milk is added to it then the ratio of water to milk becomes 1 : 4. Find the initial quantity of mixture ?

Accepted Answer

From the given data, let the initial quantity of the mixture = 5x Then, 2 x - 16 3 x - 24 + 40 = 1 4 8 x - 64 = 3 x + 16 5 x = 80 x = 16 lit Then the initial quantity of the mixture = 5x = 5 x 16 = 80 lit.

Question 10

From a container of wine, a thief has stolen 15 liters of wine and replaced it with same quantity of water.He again repeated the same process. Thus in three attempts the ratio of wine and water became 343:169. The initial amount of wine in the conta…

Accepted Answer

W i n e ( l e f t ) W a t e r ( a d d e d ) = 343 169 It means W i n e ( l e f t ) W i n e ( i n i t i a l a m o u n t ) = 343 512 ∵ 343 + 169 = 512 Thus , 343 x = 512 x 1 - 15 K 3 ⇒ 343 512 = 7 8 3 = 1 - 15 k 3 => K = 120 Thus the initial amount of wine was 120 liters.

Question 11

A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final m…

Accepted Answer

Milk = 3/5 x 20 = 12 liters, water = 8 liters If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters. Remaining milk = 12 - 6 = 6 liters Remaining water = 8 - 4 = 4 liters 10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters. The ratio of milk and water in the new mixture = 16:4 = 4:1 If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 x 10 = 8 liters. Amount of water removed = 2 liters. Remaining milk = (16 - 8) = 8 liters. Remaining water = (4 -2) = 2 liters. Now 10 lts milk is added => total milk = 18 lts The required ratio of milk and water in the final mixture obtained = (8 + 10):2 = 18:2 = 9:1.

Question 12

From a container of wine, a thief has stolen 15 litres of wine and replaced it with same quantity of water. He again repeated the same process. Thus, in three attempts the ratio of wine and water became 343 : 169. The initial amount of wine in the c…

Accepted Answer

w i n e ( l e f t ) w i n e ( a d d e d ) = 343 169 It means w i n e ( l e f t ) w i n e ( i n i t i a l a m o u n t ) = 343 512 (since 343 + 169 = 512) Thus, 343 x = 512 x 1 - 15 k 3 343 512 = 7 8 3 = 1 - 15 k 3 1 - 15 k = 7 8 = 1 - 1 8 Thus the initial amount of wine was 120 liters.

Question 13

A tin a mixture of two liquids A and B in the proportion 4 : 1. If 45 litres of the mixture is replaced by 45 litres of liquid B, then the ratio of the two liquids becomes 2 : 5. How much of the liquid B was there in the tin? What quantity does the …

Accepted Answer

Let the tin contain 5x litres of liquids 5 x - 45 x 4 5 5 x - 45 x 1 5 + 45 = 2 5 => 5(4x - 36) = 2(x + 36) => 20x - 180 = 2x + 72 => x = 14 litres Hence, the initial quantity of mixture = 70l Quantity of liquid B = 70 - 45 x 1 5 + 45 = 50 litres.

Question 14

In a mixture of milk and water the proportion of water by weight was 75%. If in 60 gm of mixture 15 gm water was added, what would be the percentage of water ? (Weight in gm)

Accepted Answer

Water in 60 gm mixture=60 x 75/100 = 45 gm. and Milk = 15 gm. After adding 15 gm. of water in mixture, total water = 45 + 15 = 60 gm and weight of a mixture = 60 + 15 = 75 gm. So % of water = 100 x 60/75 = 80%.

Question 15

In a 48 ltr mixture, the ratio of milk and water is 5:3. How much water should be added in the mixture so as the ratio will become 3:5 ?

Accepted Answer

Given mixture = 48 lit Milk in it = 48 x 5/8 = 30 lit => Water in it = 48 - 30 = 18 lit Let 'L' lit of water is added to make the ratio as 3:5 => 30/(18+L) = 3/5 => 150 = 54 + 3L => L = 32 lit.

Question 16

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 ∵ 20 % = 20 100 = 1 5 or 512 = K 4 5 4 Therefore, K = 1250 Hence initially the honey in the jar= 1.25 kg

Question 17

A man pays Rs. 6.40 per litre of milk. He adds water and sells the mixture at Rs. 8 per litre, thereby making 37.5% profit. The proportion of water to milk received by the customers is

Accepted Answer

Customer ratio of Milk and Water is given by Milk :: Water 6.4 0 8 1 + 3 8 = 64 11 64 11 64 10 - 64 11 => Milk : Water = 110 : 11 = 10 : 1 Therefore, the proportionate of Water to Milk for Customer is 1 : 10

Question 18

A mixture contains 25% milk and rest water. What percent of this mixture must taken out and replaced with milk so that in mixture milk and water may become equal.

Accepted Answer

Now, take percentage of milk and applying mixture rule 25 100 50 50 25 = 2 : 1 Hence required answer = 1/3 or 33.33%

Question 19

A container contains 50 litres of milk. From that 8 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 ?

Accepted Answer

Given that container has 50 litres of milk. After replacing 8 litres of milk with water for three times, milk contained in the container is: ⇒ 50 1 - 8 50 3 ⇒ 50 × 42 50 × 42 50 × 42 50 = 29.63 litres.

Question 20

4 kg of a metal contains 1/5 copper and rest in Zinc. Another 5 kg of metal contains 1/6 copper and rest in Zinc.The ratio of Copper and Zinc into the mixture of these two metals:

Accepted Answer

Copper in 4 kg = 4/5 kg and Zinc in 4 kg = 4 x (4/5) kg Copper in 5 kg = 5/6 kg and Zinc in 5 kg = 5 x (5/6) kg Therefore, Copper in mixture = 4 5 + 5 6 = 49 30 kg and Zinc in the mixture = 16 5 + 25 6 = 221 30 kg Therefore the required ratio = 49 : 221

Alligation or Mixture Questions