An average, or an arithmetic mean, is the sum of 'n' different data divided by 'n'
Points to remember:
1 . Age of new entrant = New average + No. of old members x change in average
2 . Age of one who left = New average - No. of old members x change in average
3 . Age of new person = Age of the removed person + No. of members x change in average In all the above three cases, if there is a decrease in the average, the sign of change in average will be negative.
4 . If a certain distance is covered at x km/hr
and the same distance is covered by y km/hr,
then the average speed during the whole journey
is
1 . The average age of 30 boys of a class is
equal to 14 years. When the age of the class
teacher is included the average becomes 15
years. Find the age of the class teacher?
Total age of 30 boys = 14x30=420 years
Total age when the teacher is included
= 15x31 = 465 years
Therefore Age of the class teacher
= 465 - 420 = 45 years
Direct Formula
Age of new entrant = New average + No.
of old members x change in average
= 15+30(15-14) = 45 years.
2 . The average weight of 8 men is increased
by 1.5 g. when one of the men who weighs
65 kg is replaced by a new man. The weight
of the new man is?
A: Weight of the new man = Weight of the man
replaced + (Number x change in average)
= 65 + (8x1.5) = 65+12 = 77 kg.
3 . The average of 11 results is 50. If the
average of first six results is 49 and that of
last six is 52, find the sixth result?
A: The sum of 11 results = 11x50 = 550
The sum of first 6 results = 6x49 = 294
The sum of last 6 results = 6x52 = 312
Sixth results = 294+312-550 = 56
4 . There were 35 students in a hostel. If
the number of students increased by 7, the
expenses of the mess were increased by Rs.
42 per day, while the average expenditure per
head diminished by Re. 1. The original expenditure
of the mess was?
Ans: Let the original expenditure per head be
Rs. x.
Then 35x + 42 = (x-1) 42
35x + 42 = 42x - 42 or x = 12
5 . The average expenditure of a man for the
first five months was Rs. 120 and for the next
seven months is Rs. 130. What was his
monthly average income if he saved Rs. 290
in that years?
Total income for 12 months.
= Rs. (120x5+130x7+290)
= Rs. 1800
Average monthly income
= 1800/12
= Rs.150
1 . The marks obtained by a student in five
subjects are 68,73,62,85 and 79. Find the
average score?
1) 73 2) 73.4
3) 75 4) 74.5
2 . The average income of a group of 9 workers
is Rs. 137.30 and that of another group of
7 workers is Rs. 95.06. The average income
of all the persons is:
1) Rs. 118.82 2) Rs. 116.18
3) Rs. 125.18 4) Rs. 128.15
3 . There are 40 boys in a class. One boy
weighing 40 kg goes away, and at the same
time another boy joins the class. If the average
weight of the class is thus increased by
100 gm, the weight of the new boy is.
1) 39.9 kg 2) 44.1 kg
3) 40.1 kg 4) 44 kg
4 . My average expenses for 4 days is Rs.
6.00. I spend Rs. 7.70 on first day and Rs.
6.30 on second day. If I spent Rs. 10 on third
day, what did I spend on the 4th day?
1) Rs. 2/- 2) Rs. 3/-
3) Rs. 4/- 4) Nothing
5 . The average temperature on Tuesday,
Wednesday and Thursday was 37° centigrade.
The average tempeature on Wednesday,
Thursday and Friday was 38° centigrade. If
the temperature on Friday was 39° centigrade,
the temperature on Tuesday was:
1) 35° C 2) 36° C
3) 37° C 4) 38° C
6 . The average age of students in two
classes of 40 students each is 10 years and 8
years respectively. The average age of students
in both the classes taken together is:
1) 8 years 2) 9 years
3) 10 years 4) 11 years
7 . The average age of 50 soldiers in troop
is 25 years. If the captain's age is included,
the average age of all of them still remains
the same. What is the captain's age in years?
1) 25 2) More than 25
3) Less than 25 4) Cannot be
determined
8 . Two towns A and B are some distance
apart. A girl cycles from A to B at a speed of
10 km/hr and then back from B to A at the
rate of 15 km/ hr. The average speed during
the journey is:
1) 12.5 km/hr 2) 15 km/hr
3) 12 km/hr 4) 13.5 km/hr
9 . An employee's average contribution to
his provident fund for the first 9 months was
Rs. 3,500 each and for each of the remaining
3 months, the contribution was Rs. 5,500. By
what amount was his total contribution short
of Rs. 58,000?
1) Rs. 4,000 2) Rs. 16,500
3) Rs. 8,000 4) Rs. 10,000
10. What fraction must be subtracted from
the sum of
1/4 and 1/6 to have an average of 1/12 of these the two fractions?
1) 1/3 2) 1/2 3)1/4 4)1/8
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