AVERAGES
Concept of Weighted Average: When we have 2 or more groups whose individual averages are known, then to find the
combined average of all the elements of all the groups we use weighted average. Thus, if we have k groups with averages
A1, A2 .... Ak and having n1, n2 .... nk elements then the weighted averages is given by the formula :
Ex. 1 A school has only 3 classes that contain 10, 20 and 30 students respectively. The pass percentage of these
classes are 20%, 30%, and 40% respectively. Find the pass percentage of the entire school
sol. Using weighted average:
Alternatively, we can also use solving-while-reading as recognize that the pass percentage would be
As soon as you get into the second line of the question, get back to the first sentence and get the total
number of passed students = 2 + 6 + 12 and you are through with the problem.
ASSIGNMENT
1. The average age of 24 students and the principal is 15 years. When the principal’s age is excluded, the
average age decreases by 1 year. What is the age of the principal ?
(A) 38 (B) 40
(C) 39 (D) 37
(E) Data inadequate
2. The average weight of 3 men A, B and C is 84 kg. Another man D joins the group and the average now becomes
80 kg. If another man E, whose weight is 3 kg more than that of D, replaces A then the average weight of B, C, D
and E becomes 78 Kg. The weight of A is
(A) 70 kg (B) 72 kg
(C) 79 kg (D) 78 kg
(E) 80 kg
3. The mean temperature of Monday to Wednesday was 37°C and of Tuesday to Thursday was 34°C.
If the temperature on Thursday
as 4/5 that of Monday, the temperature on Thursday was
(A) 38° C (B) 36°C
(C) 40°C (D) 39°C
(E) None of these
4. Three years ago, the average age of A, B and C was 27 years and that of B and C 5
years ago was 20 years. A’s present age is
(A) 30 years (B) 35 years
(C) 40 years (D) 48 years
(E) None of these
5. Ajit Tendulkar has a certain average for 9 innings. In the tenth inning, he scores 100 thereby
increasing his average by 8 runs. His new average is
(A) 20 (B) 24
(C) 28 (D) 32
(E) 36
6. The average of 13 papers is 40. The average of the first 7 papers is 42 and of the last seven
papers is 35. Find the marks obtained in the 7th paper ?
(A) 23 (B) 38
(C) 19 (D) 39
(E) None of these
7. The average age of the Indian cricket team playing the Nagpur test is 30. The average age of 5 of the players is 27 and that of another
set of 5 players, totally different from the first five, is 29 If it is the captain who was not included in either of these two groups,
then find the age of the captain.
(A) 75 (B) 55
(C) 50 (D) 58
(E) Cannot be determined
8. Siddhartha has earned an average of 4200 dollars for the first eleven months of the years. If the justifies his staying on
in the US on the basis of his ability to earn at least 5000 dollars per month for the entire year, how much should he earn
(in dollars) in the last month to achieve his required average for the whole year ?
(A) 14600 (B) 5800
(C) 12800 (D) 1300
(E) 13800
9. A bus goes to Ranchi from Patna at the rate of 60 km per hour. Another bus leaves Ranchi for Patna at the same time as
the first bus at the rate of 70 km per hour. Find the average speed for the journeys of the two buses combined
if it is known that he distance from ranchi to patna is 420 kilometers.
(A) 64.615 kmph (B) 64.5 kmph (C) 63.823 kmph (D) 64.82 kmph
(E) None of these
10. A train travels 8 km in the first quarter of an hour, 6 km in the second quarter and 40 km in the third quarter.
Find the average speed of the train per hour over the entire journey.
(A) 72 km/h (B) 18 km/h
(C) 77.33 km/h (D) 78.5 km/h
(E) 79 kg/hr
11. The average salary per head of all the workers in a company is Rs. 95. The average salary of 15 officers is Rs. 525 and
the average salary per head of the rest is Rs. 85. Find the total number of workers in the workshop.
(A) 660 (B) 580
(C) 650 (D) 460
12. The average age of 8 men is increased by 2 years when one of them whose age is 24 years is replaced by a woman. What is the age of the woman ?
(A) 35 years (B) 28 years
(C) 32 years (D) 40 years
13. The Average monthly expenditure of Ravi was Rs. 1100 during the first 3 months, Rs. 2200 during the next 4 months
and Rs. 4620 during the subsequent five months of the year. If the total saving during the year was Rs. 2100, find Ravi’s average monthly income.
(A) Rs. 1858 (B) Rs. 3108.33 (C) Rs. 3100 (D) None of these
14. Shyam bought 2 articles for Rs. 5.50 each, and 2 articles for Rs. 3.50 each, and 3 articles for Rs. 5.50 each and 5 articles for
Rs. 1.50 each. The average price for one article is
(A) Rs. 3 (B) Rs. 3.10
(C) Rs. 3.50 (D) Rs. 2
15. In a bag, there are 150 coins of Rs. 1,50 p and 25 p denominations. If the total value of coins is Rs. 150, then find how many rupees can be constituted by 50 p coins.
(A) 16 (B) 20
(C) 28 (D) None of these
16. With an average speed of 40 km/h, a train reaches its destination in time. If it goes with an average speed of 35 km/h, it is late by
15 minutes. The length of the total journey is :
(A) 40 km (B) 70 km
(C) 30 km (D) 80 km
(E) 60 km
17. In the month of July of a certain year, the average daily expenditure of an organisation was Rs. 68. For the first 15 days
of the month, the average daily expenditure was Rs. 85 and for the last 17 days, Rs. 51. Find the amount spent by the
organisation onthe 15th of the month.
(A) Rs. 42 (B) Rs. 36
(C) Rs. 34 (D) Rs. 52
(E) Rs. 40
18. In 1919, W. Rhodes, the Yorkshire cricketer, scored 891 runs for his county at an average of 34.27; in 1920, he scored
949 runs at an average of 28.75; in 1921, 1329 runs at an average of 42.87 and in 1922, 1101 runs at an average of 36.70.
What was his county batting average for the four years ?
(A) 36.23 (B) 37.81
(C) 35.58 (D) 28.72
(E) None of these
19. A train travels with a speed of 20 m/s in the first 10 minutes, goes 8.5 km in the next 10 minutes, 11 km in the next
10, 8.5 km in the next 10 and 6 km in the next 10 minutes. What is the average speed of the train in kilometer per hour for the jounrey described ?
(A) 42 kmph (B) 35.8 kmph (C) 55.2 kmph
(D) 46 kmph (E) 52 kmph
20. One-fourth of a certain journey is covered at the rate of 25 km/h, one-third at the rate of 30 km/h and the rest at 50 km/h. Find the
average speed for the whole journey.
(A) 600/53 km/h (B) 1200/53 km/h (C) 1800/53 km/h (D) 1600/53
(E) None of these
21. If the fifth down batsman gets out for a duck, then find the average runs scored by the first six batsmen.
(A) 67.1 (B) 63.3
(C) 48.5 (D) Cannot be determined
22. The weight of a body as calculated by the average of 7 different experiments is 53.735 gm. The average of the
first three experiments is 54.005 gm, of the fourth is 0.004 gm greater than the fifth, while the average of the sixth and
seventh experiment was 0.010 gm less than the average of the first three. Find the weight of the body obtained by the fourth experiment.
(A) 4k9.353 gm (B) –5.0866% (C) 12.5% (D) None of these
23. A certain number of trucks were required to transport 60 tons of steel wire from the TISCO factory in jamshedpur.
However, it was found that since each truck could take 0.5 tons of cargo less, another 4 trucks were needed. How many
trucks were initially planned to be used ?
(A) 10 (B) 15
(C) 20 (D) 25
24. One collective farm got an average harvest of 21 tons of wheat and another collective farm that had 12 acres of land less
given to wheat, got 25 tons from a hectare. As a result, the second farm harvested 300 tons of wheat more than the first.
How manytons of wheat did each farm harvest ?
(A) 3150.3450 (B) 3250,3550 (C) 2150,2450 (D) None of these
Directions for Questions 25 – 35: Read the following :
There are 3 classes having 20, 25 and 30 students respectively having average marks in an examination as 20, 25 and 30
respectively. If the three classes are represented by A, B and C and you have the following information
about the three clases, answer the questions that follow :
A ® Highest score 22, Lowest score 18
B ® Highest score 31, Lowest score 23
C ® Highest score 33, Lowest score 26
If five students are transferred from A to B.
25. What will happen to the average score of B ?
(A) Definitely increase (B)Definitely decrease
(C) Remain constant (D) Cannot say
26. What will happen to the average score of A?
(A) Definitely increase (B)Definitely decrease
(C) Remain constant (D) Cannot say
In a transfer of 5 students from A to C
27. What will happen the average score of C ?
(A) Definitely increase (B) Definitely decrease
(C) Remain constant (D) Cannot say
28. What will happen to the average score of A?
(A) Definitely increase (B) Definitely decrease
(C) Remain constant (D) Cannot say
In a transfer of 5 students from B to C
29. What will happen to the average score of C?
(A) Definitely increase (B) Definitely decrease
(C) Remain constant (D) Cannot say
30. which of these can be said about the average score of B ?
(A) Increases if C decreases
(B) Decreases if C increases
(C) Increases if C decreases
(D) Decreases if C decreases
(E) Cannot say
31. In a transfer of 5 students from A to B, the maximum possible average achievable for group B is
(A) 25 (B) 24.5
(C) 20.75 (D) 24
(E) Cannot be determined
32. For the above case, the maximum possible average achieved for group A will be
(A) 20.66 (B) 21.5
(C) 20.75 (D) 20.5
(E) Cannot be determined
33. If 5 students are transferred from B to A, what will be the minimum possible average of A ?
(A) 19.55 (B) 21.5
(C) 19.33 (D) 20.5
(E) Cannot be determined
34. If 5 students are transferred from B to A, what will be the minimum possible average of A ?
(A) 20.69 (B) 21
(C) 20.75 (D) 20.6
(E) 21.2
35. For questiozn 34, what will be the maximum average of A ?
(A) 23.2 (B) 22.2
(C) 18.75 (D) 19
(E) Cannot be determined
Directions for Question 36–41 : Read the following and answer the question that follow.
If 5 people are transferred from A to B and another independent set of 5 people are transferred back from B to A, then after
this operation (Assume that the set transferred from B to A contains none from the set of students that came to B from A)
36. What will happen to B’s average ?
(A) Increase if A’s average decreases
(B) Decrease always
(C) Cannot be said
(D) Decrease if A’s average decreases
(E) Increase if A’s average increases
37. What can be said about A’s average ?
(A) Will decrease
(B) Will always increase if B’s average changes
(C) May increase or decrease
(D) Will increase only if B’s average decrease
(E) Will decrease only if B’s average increase
38. At the end of the 2 steps mentioned above
(in the direction) what could be the maximum value of the average of class B ?
(A) 25.4 (B) 25
(C) 24.8 (D) 24.6
(E) 25.2
39. For question 38, what could be the minimum value of the average of class B ?
(A) 22.4 (B) 24.2
(C) 25 (D) 23.l75
(E) None of these
40. What could be the maximum possible average achieved by class A at the end of the operation?
(A) 25.2 (B) 26
(C) 2325 (D) 23.75
(E) None of these
41. What could be the minimum possible average of class A at the end of the operation ?
(A) 21.4 (B) 19.2
(C) 28.5 (D) 20.25
(E) 20.4
ANSWERKEY
1) C 2) C 3) B 4) C 5) C 6) C 7) C 8) E 9) A 10) A 11) A 12) D
13) B 14) C 15) D 16) B 17) C 18) C 19) C 20) C 21) D 22) C 23) C
24) A 25) B 26) D 27) B 28) D 29) D 30) B 31) B 32) A
33) C 34) D 35) B 36) B 37) B 38) C 39) A 40) C 41) D