Presentation on concepts in quantitative aptitudes (Average, Height & Distance)

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Average, Height & Distance
Empowering through Skill Development

2. Definition of AverageDefinition of Average
Average is the number that is found by dividing the sum of data by the
number of items in the dataset. It is also called the “mean”.
Example:
The average height of students in the class is 160 cms.
This average was found by adding the height of all students in the class and
then dividing that sum by the total number of students.
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then dividing that sum by the total number of students.
Exercise:
Find the average of 20, 45, 68, 40, 15
SUM = 20+45+68+40+15 = 188
Average = SUM/5 = 188/5 = 37.6

3. Facts to RememberFacts to Remember
If each no. is increased or decreased by the same quantity, then the average
(mean) also increases or decreases by the same quantity.
If each no. is multiplied or divided by the same quantity, then the average
(mean) also gets multiplied or divided by the same quantity.
If the same value is added to half of the quantities and same value is
subtracted from the other half of the quantities, then there will not be any
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subtracted from the other half of the quantities, then there will not be any
change in the final value of the average.
The average of consecutive m odd/even no. = 1st No + (m-1) [m is count of nos.]
or (1st No. + Last No.)/2
The lowest no = average – (m-1) = the greatest no – 2*(m-1)
The greatest no = average + (m – 1) = a + 2*(m-1) [a is first no.]

4. SolveSolve
If the average of consecutive 26 odd nos. is 100, then find the lowest no.?
The sum of the ages of students in a class is 210. If there are 60
students in the class, find the average age of students in that class.
a) 3.4 yrs b) 3.5 yrs c) 3.55 years d) 3.65 yrs
Average age = 210/60 = 3.5 years
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a) 65 b) 70 c) 75 d) 80
Lowest no = average – (m-1) = 100 – (26 – 1) = 75
Find the average of consecutive odd no from 1 to 13?
a) 6 b) 6.5 c) 7 d) 8
Average = 1 + (7 – 1)= 7 or Average = (1 + 13)/2 = 7

5. SolveSolve
There are 48 workers in any office having average salary as Rs. 5375. If
the monthly income of manager is included then average salary of
worker is increased by Rs 55. Then find the manager’s salary?
a) 8070 b) 9080 c) 7550 d) 8080
Manager’s salary = 5375 + (48+1)x55 = 8070
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The average age of 45 students and a teacher is 13 years. If teacher’s
age is excluded then average age is decreased by 4 months then find
the age of teacher?
a) 26 b) 28 c) 30 d) 32
Teacher’s age = 13 + (46-1)x4/12 = 28

6. SolveSolve
A student tries to find out the average temperature of 25 days which
comes out 28.96°C. But he has considered 24°C instead of 42°C and
28°C instead of 18°C by mistake then find the real average
temperature?
a) 29.28 ºC b) 30.24 ºC c) 28.56 ºC d) None of these
Difference in temp. = (24-42) + (28-18) = -8 ºC
Avg. Temp. = 28.96 + 8/25 = 29.28 ºC
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There are 8 member in a family having average age 24 years. If Shyam
is included in this family after replacing Ravi then average age is 22
years. If the sum of both ages is 64 years then find the age of Shyam?
a) 26 b) 24 c) 30 d) 32
Ravi – Shyam = 8(24-22) = 8×2 = 16
R – S = 16 and R + S = 64 ; after solving these two equations
2R = 80 and R = 40 years
Thus Age of Shyam = 64 – 40 = 24 years.

7. Weighted AverageWeighted Average
Calculate the average percentage of marks of both the sections of class (5A
& 5B) when both the sections have 60% and 70% average marks.
If your answer is 65% then it is wrong because you don’t know the number
of students in each section. So to calculate Weighted Average, we have to
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of students in each section. So to calculate Weighted Average, we have to
know the number of students in each section.
Let 5A has 40 Students and 5B has 60 Students, then the average is
(40*0.6 + 60*0.7)/(40+60) = 66%

8. Weighted AverageWeighted Average ((contdcontd…..)…..)
Prob.: A student is enrolled in a biology course where the final grade is
determined based on the following categories: tests 40%, final exam 25%,
quizzes 25%, and homework 10%. The student has earned the following
scores for each category: tests-83, final exam-75, quizzes-90, homework-
100. Calculate the student's overall grade.
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Ans . (83 * .40) + (75 * .25) + (90 * .25) + (100 * .10) = 33.2 + 18.75 + 22.5 + 10
= 84.45 or 84% if rounded down.

9. Height & DistanceHeight & Distance
H ----- Height
θ ------ Angle of Elevation
x ------ Distance
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Angle of Depression

10. Height & DistanceHeight & Distance ((contdcontd….)….)
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11. SolveSolve
If the distance of a person from a tower is 100 m and the angle
subtended by the top of the tower with the ground is 45o, what is the
height of the tower in meters?
a) 80 m b) 85 m c) 90 m d) 100 m
Height = 100*Tan45 = 100 meter
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A little boy is flying a kite. The string of the kite makes an angle of 30o with
the ground. If the height of the kite is 12 m, find the length (in meters) of
the string that the boy has used.
a) 6 m b) 12 m c) 24 m d) None of these
Length of the string = 12/Sin30º = 24 m

12. SolveSolve
Two men on the same side of a tall building notice the angle of
elevation to the top of the building to be 30o and 60o respectively. If the
height of the building is known to be h =110 m, find the distance (in
meters) between the two men.
a) 127 b) 135 c) 118 d) None of these
Distance = 110/Tan30º – 110/Tan60º = 127
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From the top of a 7 m high building, the angle of elevation of the top of
a cable tower is 60° and the angle of depression of its foot is 45°.
Determine the height of the tower.
AB = 7 m = BC = AD
EC = ED + DC
= 7*Tan60 + 7

13. SolveSolve
The angle of elevation of the sun, when the length of the shadow of a
tree 1.732 times the height of the tree, is:
a) 30º b) 45º c) 60º d) None of these
AC = AB x Sq.Root(3) ; Tanθ = AB/AC
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The angle of elevation of an aeroplane from a point on ground is 60º.
After 15 seconds, the angle of elevation changes to 30º. If the plane is
flying at a height of 1000 meters, find the speed of the plane.
1000 m60
30
z y
x
y = x – z meters
Speed = y/15 m/s