**Ex.1:Find the average of all prime numbers between 30 and 50?**

**Sol:**there are five prime numbers between 30 and 50.

They are 31,37,41,43 and 47.

Therefore
the required average=(31+37+41+43+47)/5 ó199/5 ó 39.8.

**Ex.2. find the average of first 40 natural numbers?**

**Sol:**sum of first n natural numbers=n(n+1)/2;

So,sum
of 40 natural numbers=(40*41)/2 ó820.

Therefore the required average=(820/40) ó20.5.

**Ex.3. find the average of first 20 multiples of 7?**

**Sol:**Required average =7(1+2+3+…….+20)/20 ó(7*20*21)/(20*2) ó(147/2)=73.5.

**Ex.4. the average of four consecutive even numbers is 27. find the largest of these**

**numbers?**

**Sol:**let the numbers be x,x+2,x+4 andx+6. then,

(x+(x+2)+(x+4)+(x+6))/4) =
27

ó(4x+12)/4 = 27

óx+3=27 ó
x=24.

Therefore the largest
number=(x+6)=24+6=30.

**Ex.5. there are two sections A and B of a class consisting of 36 and 44 students respectively. If the average weight of section A is 40kg and that of section B is 35kg, find the average weight of the whole class?**

**Sol:**total weight of(36+44) students=(36*40+44*35)kg =2980kg.

Therefore
weight of the total class=(2980/80)kg
=37.25kg.

**Ex:6.nine persons went to a hotel for taking their meals 8 of them spent Rs.12 each on their meals and the ninth spent Rs.8 more than the average expenditure of all the nine.What was the total money spent by them?**

**Sol:**Let the average expenditure of all nine be Rs.x

Then 12*8+(x+8)=9x or 8x=104 or
x=13.

Total money spent =
9x=Rs.(9*13)=Rs.117.

**Ex.7: Of the three numbers, second is twice the first and is also thrice the third.If the average of the three numbers is 44.Find the largest number.**

**Sol**: Let the third number be x.

Then second number = 3x.

First number=3x/2.

Therefore x+3x+(3x/2)=(44*3) or
x=24

So largest number= 2

^{nd}number=3x=72.**Ex.8:The average of 25 result is 18.The average of 1**

^{st}12 of them is 14 & that of last 12 is 17.Find the 13^{th}result.**Sol**: Clearly 13

^{th}result=(sum of 25 results)-(sum of 24 results)

=(18*25)-(14*12)+(17*12)

=450-(168+204)

=450-372

=78.

**Ex.9:The Average of 11 results is 16, if the average of the 1**

^{st}6 results is 58 & that of the last 63. Find the 6^{th}result.**Sol**: 6

^{th}result = (58*6+63*6-60*11)=66

**Ex.10:The average waight of A,B,C is 45 Kg. The avg wgt of A & B be 40Kg & that of B,C be 43Kg. Find the wgt of B.**

**Sol.**Let A,B,c represent their individual wgts.

Then,

A+B+C=(45*3)Kg=135Kg

A+B=(40*2)Kg=80Kg &
B+C=(43*2)Kg=86Kg

B=(A+B)+(B+C)-(A+B+C)

=(80+86-135)Kg

=31Kg.

**Ex. 11. The average age of a class of 39 students is 15 years. If the age of the teacher be included, then the average increases by3 months. Find the age of the teacher.**

**Sol.**Total age of 39 persons = (39 x 15) years

=
585 years.

Average age of 40 persons= 15 yrs 3 months

= 61/4 years.

Total age of 40 persons =

__(_(61/4 )__x 40) years= 610 years.
:. Age of the teacher = (610 - 585) years=25
years.

**Ex. 12. The average weight of 10 oarsmen in a boat is increased by 1.8 kg when one of the crew, who weighs 53 kg is replaced by a new man. Find the weight of the new**

**man.**

**Sol.**Total weight increased =(1.8 x 10) kg =18 kg.

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

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