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= 2nd number=3x=72.
Ex.8:The average of 25 result
is 18.The average of 1st 12 of them is 14 & that of last 12 is
17.Find the 13th result.
Sol: Clearly 13th 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 1st
6 results is 58 & that of the last 63. Find the 6th result.
Sol: 6th 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.
Ex. 13. There were 35
students in a hostel. Due to the admission of 7 new students, ;he expenses of
the mess were increased by Rs. 42 per day while the average expenditure per
head diminished by Rs 1. Wbat was the original expenditure of the mess?
Sol. Let the original
average expenditure be Rs. x. Then,
42 (x - 1) - 35x=42 ó 7x= 84 ó x =12.
Original expenditure = Rs.
(35 x 12) =Rs. 420. .
14. A batsman makes a score
of 87 runs in the 17th inning and thus increases his avg by 3. Find his average
after 17th inning.
Sol. Let the average
after 17th inning = x.
Then, average after 16th inning = (x -
3).
:. 16 (x - 3) +
87 = 17x or x = (87 - 48) = 39.
Ex.15. Distance between two
stations A and B is 778 km. A train covers the journey from A to B at 84 km per
hour and returns back to A with a uniform speed of 56 km perhour. Find the
average speed of the train during the whole journey.
Sol. Required average
speed = ((2xy)/(x+y)) km / hr
=(2 x 84 x 56)/(84+56)km/hr
= (2*84*56)/140 km/hr
=67.2 km/hr.
