Averages Question Sheet (Weighted Average)

Table Of Content

Practice Question

Answer Key

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Averages Question Sheet (Weighted Average)

Q.1. 6 liters of pure milk are added to 10 liters of a mixture of water and milk having 40% milk. What is the percentage of milk in the resulting solution?

1. 50%  

2. 62.5%

3. 75% 

4. 87.5%

Q.2 Mixture of alcohol and water contains 35% of alcohol by volume. Then, 40 ml of water is added to such a mixture of 100 ml. The percentage of alcohol in the new mixture is

1. 35%

2. 30%

3. 25%

4. 20%

Q.3 A man bought three varieties of mangoes. He bought  3 dozen of variety A at Rs 120 per dozen, 4 dozen of variety B at Rs 160 per dozen and ‘x’ dozen of variety C at Rs 115 per dozen. If the average price per dozen was Rs. 128, find ‘x’.

1. 10

2. 11

3. 9

4. 8

Q.4 The average wage of a worker during a fortnight comprising 15 consecutive working days was Rs. 90 per day. During the first 7 days, his average wage was Rs. 87/day and the average wage during the last 7 days was 92/day. What was his wage on the 8th day?

1. 90

2. 92

3. 96

4. 97

Q.5 The average Score of 21 students of class “X A” in a school is 43 marks, while the average score of 28 students of class “X B” of the same school is 36 marks. What is the average score of all the students put together.

1. 38

2. 41

3. 42

4. 39

Q.6 In group ‘A’ - 12 students have 87 marks each; in group B - 18 students have 82 marks each; in group ‘C’ - 21 students have 91 marks each and in group ‘D’- 7 students have 94 marks each. What is the average score of all four groups?

1. 87.74 cm

2. 88.78 cm

3. 89.17 cm

4. 90.49 cm

Q.7 Two jars of capacity 3 and 5 litres are filled with mixtures of wine and water. In the smaller jar 25% of the mixture is wine and in the larger jar 25% of the mixture is water. The jars are emptied into a nine litre cask which is then topped up with water. What is the percentage of win in the cask?

1. 
   

2. 25%

3. 50%

4. 12.5%

5. None of these

Q.8 A person buys rice of three different varieties at ₹ 60, ₹ 50, and ₹ 40 per kg, respectively, and the quantities bought are in the proportion 1 : 4 : 5. He mixes all the rice and sells half of the mixture at ₹ 60 per kg. The price, in ₹ per kg, at which he should sell the remaining rice, to make an overall profit of 25%, is

1. 52

2. 53

3. 54

4. 55

Q.9 Sugar worth Rs. 110 per kg and Rs. 121 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 138 per kg, the price of the third variety per kg will be :

1. Rs. 160

2. Rs. 160.50

3. Rs. 170

4. Rs. 276 + 138

Q.10 In an alloy, the ratio of copper and zinc is 5 : 2. If 1.25 kg of zinc is mixed in 17 kg 500 gm of alloy, then the ratio of copper and zinc in the alloy will be: 

1. 1 : 2

2. 2 : 1

3. 2 : 3

4. 3 : 2

Q.11 A shopkeeper mixes three varieties of sugar worth Rs.25/kg, Rs.20/kg and Rs.30/kg and sells the mixture at a profit of 25% at Rs. 30/kg. How many kg of the second variety will be in the mixture if 2 kg of the third variety and 4 kg of first variety is there in the mixture?

1. 3 kg

2. 4 kg

3. 6 kg

4. 7 kg

Q.12In what ratio must a person mix three kinds of tea costing Rs.60/kg, Rs.75/kg and Rs.100 /kg so that the resultant mixture when sold at Rs.92/kg yields a profit of 15%?

1. 1 : 4 : 2

2. 3 : 7 : 6

3. 1 : 2 : 4

4. None of these

Q.13 10 years ago, the average age of a newly-wed couple was 25. 5 years ago, the average age of the man, his wife and their son was 21. At present, the average age of the man, his wife, their son and their daughter is 20. What is the age difference (in years) between the son and the daughter?

1. 6 years

2. 8 years

3. 7 years

4. 5 years

Q.14 There are two casks, the second is thrice as big as the first. The first cask contains wine and water in the ratio 2 : 3 and the second contains wine and water in the ratio 7 : 8. The contents of the two casks are added to the third cask which can hold four times as much liquid as the first. What is the ratio of water and wine in the third cask?

1. 9 : 11

2. 33 : 72

3. 44  : 81

4. 11: 9

Q.15 A mixture of milk and water contains 80% milk. If 146 litres of water is added to the mixture, then the quantity of water becomes 94 litres less than the quantity of milk in the resultant mixture. What was the initial quantity of the mixture?

1. 320 L

2. 400 L

3. 480 L

4. 540 L

Q.16 Two jars of capacity 3 and 5 litres are filled with mixtures of wine and water. In the smaller jar 25% of the mixture is wine and in the larger jar 25% of the mixture is water. The jars are emptied into a nine litre cask which is then topped up with water. What is the percentage of wine in the cask?

1. 12.5%

2. 25%

3. ’50%

4. 60%

Q.17 In a class of 40 students, the number of boys is 4 more than the number of girls. The average weight of the entire class is 48.4 Kg. If the average weight of girls is 44 Kg, what is the average weight of boys?

1. 50

2. 51

3. 52

4. 53

Q.18 There are 3 jars containing a mixture of milk and water. The ratio of volumes of mixtures in 3 jars is 5 : 6 : 9. In the first jar ratio of milk and water is 2 : 3, in the second it is 5 : 1 and in the third container it is 4 : 5. If all the contents are mixed together then what is the resultant ratio of milk and water?

1. 5 : 3

2. 7 : 2

3. 7 : 9

4. 11 : 9

C

Q.20 Three vessels have volume in the ratio of 2 : 3 : 7. These vessels are full of mixture of milk & water. First vessel has milk & water in the ratio of 3 : 2, second has milk & water in the ratio of 1 : 4 and third has milk & water in the ratio of 9 : 1. What will be the resultant ratio of milk & water if these liquids are poured in a big container?

1. 23 : 13

2. 25 : 13

3. 27 : 13

4. 28 : 13

Q.21 In an office the average age of all the female employees is 21 years and that of male employees is 32 years. If the average age of all the employees is 27 years and the difference between male and female employees is 12 then find the total number of employees in the office.

1. 96

2. 108

3. 120

4. 132

Q.22 There are three varieties of wheat costing Rs.10, Rs.12 and Rs.14 per kg. Which one of the following represent the ratio in which the three varieties are mixed, if the cost price of the mixture is Rs.13? 

1. 1 : 1 : 2

2. 1 : 2 : 3

3. 1 : 1 : 4

4. None of these

Q.23 The ratio of 'metal 1' and 'metal 2' in Alloy 'A' is 3 : 4. In Alloy 'B' same metals are mixed in the ratio 5 : 8. If 26 kg of Alloy 'B' and 14 kg of Alloy 'A' are mixed, then find out the ratio of 'metal 1' and 'metal' 2' in the new Alloy.

1. 2 : 3

2. 3 : 2

3. 2 : 5

4. 5 : 2

Q.24 Three glasses of equal volumes are filled with a mixture of spirit and water in the ratio 2:5, 3:4, 4:5. They are emptied into a vessel. Find the proportion of spirit and water. 

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Frequently Asked Questions — Averages for CAT & IPMAT 2026

What is the average formula?

Average = Sum of all values / Number of values. Equivalently, Sum = Average × Number of values. This basic identity is used to find missing values: if average of n numbers is A and a new number x is added, new average = (n×A + x)/(n+1).

What is the weighted average formula?

Weighted Average = (w1×x1 + w2×x2 + ... + wn×xn) / (w1+w2+...+wn). Used when different items have different weights/frequencies. Example: if 30 students score avg 70 and 20 students score avg 80, combined avg = (30×70 + 20×80)/50 = (2100+1600)/50 = 74.

How does adding/removing a number affect the average?

If a number x is added to a set of n numbers with average A: new average = A + (x-A)/(n+1). If x > A, average increases; if x < A, average decreases. This deviation method is faster than recalculating the full sum.

What is the deviation method for averages?

Assume any convenient number as the assumed mean. Find deviations of each value from this mean. Average = Assumed Mean + (Sum of deviations / n). This method is especially fast when numbers are close together, as deviations are small.

How do I solve 'average of first n natural numbers' problems?

Average of first n natural numbers = (n+1)/2. Average of first n odd numbers = n. Average of first n even numbers = n+1. Average of n consecutive numbers starting from a = a + (n-1)/2. These shortcuts are frequently tested in IPMAT.

What are the most common CAT average question types?

Common types: (1) Effect of replacing one member with another on average. (2) Finding a missing value given the average. (3) Weighted average of two groups. (4) Average of an AP. (5) Cricket/sports score averages. Know all five types for CAT.

What is the average of an arithmetic progression?

For an AP, Average = (First term + Last term)/2 = Middle term. This works because terms are symmetrically distributed around the middle. For 3, 7, 11, 15, 19: average = (3+19)/2 = 11 = the middle term.

How many average questions appear in CAT and IPMAT?

Averages appear in 1-3 questions directly in CAT and 2-4 in IPMAT. They also appear embedded in DI sets as weighted average calculations. Averages form the conceptual base for alligation — mastering one topic reinforces the other.