#### Average

An average or more accurately an arithmetic mean is, in crude terms, the sum of n different data divided by n.

Averages of a group is defined as the ratio of sum of all the items in the group to the number of items in the group.

Average = (Sum of all items in the group)/ Number of items in the group.

Now, sum of all items can be ‘the sum of number of quantities like apple, people etc’ or ‘sum of values of the item like 10 coins of 2Rs each etc’.

#### Some Important Concepts:

1. Average =total of data/No.of data
2. If the value of each item is increase by the same value a, then the average of the group or items will also increase by a.
3. If the value of each item is decreased by the same value a, then the aveage of the group of items will also decrease by a.
4. If the value of each item is multiplied by the same value a, then the average of the group or items will also get multiplied by a.
5. If the value of each item is multiplied by the same value a, then the average of the group or items will also get divided by a.
6. If we know only the average of the two groups individually, we cannot find out the average of the combined group of items.
7. Average of n natural no's=(n+1)/2
8. Average of even No'=(n+1)
9. Average of odd No'= n
10. General Formula=(1st number +Last number)/2

#### 1.The average marks obtained by 120 cndidates in a certain examinationis 35.if the average marks of passed candidate is 39 and that of the failed candidates is 15,what is the number of candidates who passed the examination

(a)110    (b)115    (c)120    (d)100    (e)none of these

1. (d) Let No. of passed candidates are x So, x * 39 + (120 – x) 15= 120 * 35 x = 100

#### 2.The average age of 8 persons in a committee is increased by 2 years when two men aged 35 years and 45 years are substituted by two women.Find the average age of these two women.

(a)48    (b)36     (c)42    (d)29    (e)none of these

2.(a) Total increase = 8 * 2 = 16 years So, total age of two women = 35 + 45 +16= 96 Average age of two women=96/2=48 years

#### 3.In a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 18 years is replaced by a new boy.Find the age of new boy.

(a)19 years    (b)14 years 6 month    (c)15 years    (d)14 years 8 month     (e)12 years

3(d) Total decrease = 20 * 2 = 40 month = 3 years 4 month So, age of new boy = 18 years – 3 years 4 month = 14 years 8 month

#### 4.One -third of certain journey is covered at the rate of 25kmph,one-fourth at the rate of 30kmph and the rest at 50 kmph.Find the average speed for the whole journey.

(a)33.33 kmph    (b)36    (c)42    (d)27    (e)none of these

4.(a) Average speed = total distance / total time LCM = 3, 4 = 12 Average speed = 12 / (1/3*12*1/25 + ¼ * 12*1/30 +5/50) = 12/ (4/25 + 3/30+ 5/30 = 150*12/54 = 33.333 kmph

#### 5.The average salary of the entire staff in a office is Rs 120 per month.The average salary of officers is Rs 460 and of non officers is Rs 110. If the number of officers is 15,then find the No of non-officers in the office.

(a)480    (b)500    (c)600    (d)430    (e)510

5.(e) Let no. of non- officers be x 15 * 460 + x * 110 = (x + 15) 120 x = 510