Averages  Key Notes
Averages  Key
Notesaptitudequestionsanswersbasics
 Averages, Mixtures
and Alligation Aptitude basics, practice questions, answers and
explanations
Prepare for companies tests and interviews
 Average= (x_{1}+x_{2}+x_{3}+......x_{n})/n
where x_{1},x_{2},x_{3}, are quantities.

 Weighted Average= (n_{1}x_{1}+n_{2}x_{2}+n_{3}x_{3}+.....n_{k}x_{k})
/ n_{1}+n_{2}+n_{3}+......n_{k}
where x_{1},x_{2},x_{3}.... x_{k }are
the quality factors
n_{1},n_{2},n_{3},........n_{k} are the
quantity factors
Eg: If the
average height of boys= 172cms and that of girls=154 cms, then find average
height of the class with 18 boys and 12 girls?
 Here n_{1} and n_{2}
are no. of boys and girls (Quantity factor)
x_{1 }and x_{2} are average heights (Quality factor)

 Mixtures
For mixtures, Average, x'= (n_{1}x_{1}+n_{2}x_{2)/
(}n_{1}+n_{2})
_{
}
 Alligation:
=> n_{1}/n_{2} = (x_{2}x')/x'x_{1}
Exercise questions
1. The average wages of a worker during
a fortnight comprising 15 consecutive working days was Rs.90 per day. During
the first 7 days, his average wages was Rs.87/day and the average wages during
the last 7 days was Rs.92 /day. What was his wage on the 8th day?
a)83
b) 92
c)90
d)97
2. The average of 5 quantities is 6. The
average of 3 of them is 8. What is the average of the remaining two numbers?
a) 6.5 b)
4
c)
3
d) 3.5
3. The average temperature on Wednesday,
Thursday and Friday was 250. The average temperature on Thursday, Friday and
Saturday was 240. If the temperature on Saturday was 270, what was the
temperature on Wednesday?
a) 240
b)210
c)
270
d) 300
4. The average age of a group of 12
students is 20years. If 4 more students join the group, the average age
increases by 1 year. The average age of the new students is
a) 24
b)26
c)23
d) 22
5. When a student weighing 45 kgs left a
class, the average weight of the remaining 59 students increased by 200g. What
is the average weight of the remaining 59 students?
a) 57
kgs
b) 56.8
kgs
c)58.2 kgs
d)52.2 kgs
6. The average of 5 quantities is 10 and
the average of 3 of them is 9. What is the average of the remaining 2?
a)
11
b)
12
c)
11.5
d) 12.5
7. The average age of a family of 5
members is 20 years. If the age of the youngest member be 10 years then what
was the average age of the family at the time of the birth of the youngest member?
a)
13.5
b)
14
c)15
d) 12.5
8. Average cost of 5 apples and 4
mangoes is Rs.36. The average cost of 7 apples and 8 mangoes is Rs.48. Find the
total cost of 24 apples and 24 mangoes.
a)
Rs.1044
b) RS.2088
c)Rs.720
d) Rs.324
9. Tea worth Rs. 126 per kg and Rs. 135
per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is
worth Rs. 153 per kg, the price of the third variety per kg will be:
a) Rs.
169.50
b) Rs. 170
c) Rs. 175.50
d) Rs. 18
10. A vessel is filled with liquid, 3
parts of which are water and 5 parts syrup. How much of the mixture must be
drawn off and replaced with water so that the mixture may be half water and
half syrup?
a)
1/3
b)
1/4
c)
1/5
d) 1/7
Answer Key
1.d; 2.c; 3.d; 4.a; 5.a; 6.c; 7.d; 8.b;
9.c; 10.c