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Numerical Aptitude (Chapter: Average)

The average of a given number of quantities of the same kind is expressed as

Average = (Sum of the quantities/Number of the quantities)

Average is also called the Arithmetic Mean.

Also, Sum of the quantities = Average × Number of the quantities

Number of quantities = (Sum of the quantities/Average)

• If all the given quantities have the same value, then the number itself is the average.

• If all the given quantities are not all the same, then the average of the given quantities is always greater, than the smallest number and always less than the largest number. Equivalently, atleast one of the numbers is less than the average and atleast one is greater then the average.

• If each of the given quantities is increased by a constant p, than their average is also increased by p.

• If each of the given quantities is decreased by a constant p, then their average is also decreased by p.

• If each of the given quantities is multiplied by a constant p, then their average is also multiplied by p.

• Whenever the given quantities form an arithmetic sequence and if the given quantities has odd terms, then the average is the middle term in the sequence and if the given quantities has even terms, then the average of the sequence is the average of the middle two terms.

• In order to calculate the weighted average of a set of numbers, multiply each number in the set by the number of times it appears, add all the products and divide by the total number of numbers in the set.

• If the speed of an object from A to B is x km/h and from B to A is y km/h, then the average speed during the whole journey is (2xy/x+y) .

Example 1: Average weight of 32 students of a class is 30.5 kg. If weight of a teacher is also included then average weight is increased by 500 g. What is the weight of the teacher?

Solution. Total weight of 32 students = 30.5 × 32 = 976 kg
Average weight of (32 students + 1 teacher) = (30.5 + 0.5) = 31 kg
therefore, Total weight of (32 students + 1 teacher) = 31 × 33 = 1023 kg
therefore, Weight of teacher = (1023 – 976) kg = 47 kg

:: Home Assignment for Practice ::

1. The average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?

(a) 82 kg
(b) 85 kg
(c) 76.5 kg
(d) 80 kg

2. Sumitra has an average of 56% on her first 7 examinations. How much she should make on her eighth examination to obtain an average of 60% on 8 examinations?

(a) 88%
(b) 78%
(c) 92%
(d) 68%

3. Ages of ‘A’ and ‘B’ are in the ratio of 2 : 3 respectively. Six years hence the ratio of their ages will become 8 : 11 respectively. What is B’s present age?

(a) 18 years
(b) 28 years
(c) 27 years
(d) 25 years

 4. The total age of A and B is 12 years more than that of total age of B and C. C is how many years younger than A?

(a) C is elder than A
(b) 26
(c) 12
(d) 25

5. The average marks fetched by Mohan in History, Geography, Science and Mathematics is 10 more than the marks fetched in Mathematics. If he has got 110 marks aggregate in History and Geography, what will be the aggregate marks fetched in Science and Mathematics?

(a) 90
(b) 70
(c) 75
(d) can’t be determined

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