5.AVERAGE
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 oars
men 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 ne w
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 bats man 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.
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