Question:Find the average of all prime numbers between `30` and `50`. 

There are five prime numbers between `30` and `50`.
Thet are `31,37,43` and `47.`

`:.` Require average = `(31 + 37 + 43 + 47)/5`

`=199/5`

`=39.5`

Question:Find the average of first 30 natural numbers. 

Sum of first 30 natural numbers =`((30 xx 31)/2)` = 465
`:.` Required average = `465/30` = 15.5

Question:Find the average of first 25 multiples of 3. 

Required average = `(3(1 + 2  + 3 + ..... +25))/25`
=`((3 xx 25 xx 26)/(2 xx 25))`
=39

Question:The average age of a class of `39` students is `15` years. If the age of the teacher be included, then the average increases by 3 months. Find the age of the teacher. 

Total age of 39 persons 

`= (39 x 15)` years 

`= 585` years.

 Average age of 40 person 

`= 15` years `3` months 

`= 61/4` years.

 Total age of the 40 person 

 `= (61/4) xx 4` 

 years `= 610` years.

`:.`Total age of 40 person 

 `= (610 - 585)` 

 Years `= 25` years.

Question:The average age of a class of 39 students is 15 years. If the age of the teacher be included, then the average increases by 3 months. Find the age of the teacher? 

The total age of 39 persons =(39 x 15) years = 585 years.
Average age of 40 person =15 years 3 months =`(61/4)` years.
Total age of 40 person = `(61/4 xx 40)` years =610 years.
`:.` Age of the teacher= (610 x 585) years = 25 years.

Question:The average weight of `10` oarsmen in a boat is increased by `1.8 kg` when one of the crew, who weights `53` kg is replaced by a new man. Find the weight of the crew, who weights `53 kg` is replaced by a new man. Find the weight of the new man. 

Total weight increased 
`= (1.8 xx 10)` kg 
`=18` kg.

`:.` Weight of the new man 
`= (53 + 18 )` kg 
`=71` kg

Question:The average of 11 results is 60. If the average of first six results is 58 and the last six is 63, find the sixth result. 

Sixth result 

`= (6 xx 58 + 6 xx 63 - 11 xx 60)` 

`= 66`

Question:Distance between two stations A and B is 778 km. Hari Mohan covers the journey from A to B at 84 km per hour and return back to A with a uniform speed of 56 km per hour. Find his average speed during the whole journey. 

Required average speed = `(2xy)/(x + y)` km/hr.

= `(2 xx 84 xx 56)/(84 xx 56)` km/hr.

=`((2 xx 84 xx 56)/140)` km/hr

=67.2 km/hr

Question:There are two sections A and B of a class, considering of 36 and 44 students respectively. If the average weight of section A is 40 kg and that of section B is 35 kg, find the average weight of the whole class. 

Total weight of (36 + 44) students

 =(36 x 40 +44 x 35) kg =2980 kg.

 `:.` Average weight of the whole class =`2980/80` kg

 =37.25 kg.

Question:The average weight of A, B, C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, find the weight of the whole class. 

A + B + C = (45 x 3) kg =135 kg.
A + B = (40 x 2) =80 kg & B + C =(43 x 2) = 86 kg.
`:.` B = (A + B) + (B + C) - (A + B + C) = (86 + 80 - 135) kg = 31 kg.