1.    The average of 30 boys of a class is equal to 14 yrs. When the age of the class teacher is included the average becomes 15 yrs. Find the age of the class teacher.
(1) 45 yrs                           (2) 50 yrs
(3) 30                                 (4) 22 yrs

2.    The average weight of 4 men is increased by 3kg when one of them who weighs 120 kg is replaced by another man. What is the weight of the new man?
(1) 125 kg                          (2) 150 kg
(3) 122 kg                          (4) 132 kg

3.    The average of marks obtained by 120 candidates in a certain examination is 35. If the average marks of passed candidates is 39 and that of the failed candidates is 15, what is the number of candidates who passed the examination?
(1) 90                                 (2) 85
(3) 100                               (4) 120

4.    The average of 11 results is The average of 11 results is50. If the average of  first six results is 49 and that of last six is 52, find the sixth result?
(1) 45                                 (2) 46
(3) 55                                 (4) 56

5.    A bats man is his 17th innings makes a score of 85, and thereby increases his average by 3. What is his average after 17 innings?
(1) 40                                 (2) 36
(3) 37                                 (4) 38

6.    A train travels from A to B at the rate of 20kmper hour and from B to A at the rate of 30 km/hr. What is the average rate for the whole journey?
(1) 24 km/hr                      (2) 25 km/hr
(3) 26 km/hr                      (4) 28 km/hr

7.    The average salary of the entire staff in a office is Rs 120 per month. The average salary of officers is Rs 460 and that of non- officers is Rs 110. If the number of officers is 15, then find the number of non – officers in the office.
(1) 500                               (2) 510
(3) 520                               (4) 550
8.    There were 35 students in a hostel. If the number of students increases by 7, the expenses of the mess increase by Rs. 42 per day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess.
(1) Rs. 400                        (2) Rs. 340
(3)Rs. 420                         (4)Rs. 450

1.    Total ages of 30 boys = 14 x 30 = 420 yrs.
Total ages when class teacher is included = 15 x 31 = 465 yrs
Age of class teacher = 465 – 420 = 45 yrs.
Shortcut :
Age of new entrant = New average + No. of old members x increase in average
2.    If the average is increased by 3 kg, then sum of weights increases by 3 x 4 = 12 kg .
And this increase in weight is due to the extra weight included due to the inclusion of new person.
Weight of new man = 120 + 12 = 132 kg.

3.    Let the number of passed candidates be x. then total marks = 120 x 35 = 39x + ( 120 – x ) x 15 or, 4200 = 39x + 1800 – 15x
or, 24x = 2400  So x = 100

4.    The total of 11 results = 11 x 50 = 550
The total of first 6 results = 6 x 49 = 294
The total of last 6 results = 6 x 52 = 312
The 6th result is common to both;
Sixth result = 294 + 312  - 550 = 56

5.    Let the average after 16th innings be x, then 16x + 85
= 17 ( x + 3 ) = Total score after 17th innings.
x = 34
average after 17 innings = x + 3 = 34 + 3 = 37

6.    By the formula : average speed = (2 x 20 x 30) / (20 + 30) = 24 km/hr

7.    Let the required number of non – officers = x
Then, 110x + 460 x 15 = 120 ( 15 + x )
or, 120 x – 110 x = 460 x 15 – 120 x 15 = 15 ( 460 – 120 )
So, x = 510

8.    Suppose the average join the mess , total expenditure = 35x + 42
Now, the average expenditure = (35x + 42)/ (35 + 7) = x – 1
or, 35x + 42 = 42x – 42
or, x = 12
Thus the original expenditure of the mess = 35 x 12 = Rs. 42