## Practice Problems on Averages – Set 5

Practice Problems on Averages – Set 5
1. The average salary of all the employees in a small organization is Rs 8,000. The average salary of 7 technicians is Rs 12,000 and the average salary of the rest is Rs 6,000. The total number of employees in the organisation is?
a) 20
b) 21
c) 22
d) 25
e) 26
Explanation:
Let total number of employees be X.
Then, 8000 x X = 7 x 12000 + (X - 7) x 6000
X = 26.
Thus, the total number of employees in the organization is 26.

2. Without any stoppage, a person travels a certain distance at an average speed of 42 km/h, and with stoppages he covers the same distance at an average speed of 28 km/h. How many minutes per hour does he stop?
a) 14 min
b) 15 min
c) 26 min
d) 28 min
e) None of these
Explanation:
Let the total distance to be covered is 48 kms.
Time taken to cover the distance without stoppage = 48/42 hrs = 2 hrs
Time taken to cover the distance with stoppage = 48/28 = 3 hrs.
Thus, he takes 60 minutes to cover the same distance with stoppage.
Therefore, in 1 hour he stops for 20 minutes.

3. The average marks of a Suresh in 10 papers are 80. If the highest and the lowest scores are not considered, the average is 81. If his highest score is 92, find the lowest?
a) 55
b) 60
c) 62
d) 65
e) Can’t be determined
Explanation:
Total marks of 10 papers = 80 x 10 = 800
Total marks of 8 papers = 81 x 8 = 648
Total marks of two papers = (800 - 648) = 152
If highest total is 92, then the lowest total is
(152 - 92) = 60.

4. Three maths classes: X, Y and Z take an algebra test. The average score of class X is 83. The average score of class Y is 76. The average score of class Z is 85. The average score of class X and Y is 79 and average score of class Y and Z is 81. What is the average score of classes X, Y, Z?
a) 81.5
b) 80.5
c) 83
d) 78
e) 75
Explanation:
Let the number of students in classes X, Y and Z be A, B and C respectively.
Then, total score of X= 83A, total score of Y = 76B, total score of Z = 85C.
Also given that,
(83A + 76B) / (A + B) = 79
=>4A = 3B.
(76B + 85C)/(B + C) = 81
=>4C = 5B,
=>B = 4A/3 and C = 5A/3
Therefore, average score of X, Y, Z = ( 83A + 76B + 85C ) / (A + B + C) = 978/12 = 81.5.

5. The average of 17 numbers is 10.9. If the average of first nine numbers is 10.5 and that of the last nine numbers is 11.4, the middle number is
a) 11.8
b) 11.4
c) 10.9
d) 11.7
e) 10.7
Explanation:
Sum of first nine numbers (N1 to N9)  + Sum of last nine numbers (N9 to N17) = 10.5 x 9 + 11.4 x 9 = 21.9 x 9 = 197.1
Hence, the middle number
= 197.1 - 17 x 10.9
= 197.1 - 185.3 = 11.8

6. Suraj has a certain average of runs for 12 innings. In the 13th innings he scores 96 runs thereby increasing his average by 5 runs. What is his average after the 13th innings?
a) 48
b) 64
c) 36
d) 72
e) 68
Explanation:
To improve his average by 5 runs per innings he has to contribute 12 x 5 = 60 runs for the previous 12 innings.
Thus, the average after the 13th innings
= 96 - 60 = 36.

7. A batsman in his 17th innings makes a score of 85, and thereby increases his average by 3. What is his average after the 17th innings? He had never been ’not out’.
a) 47
b) 37
c) 39
d) 43
e) 47
Explanation:
Average score before 17th innings
= 85 - 3 × 17= 34
Average score after 17th innings
=> 34 + 3 = 37

8. The sum of three numbers is 98. If the ratio between first and second be 2 : 3 and that between second and third be 5 : 8, then the second number is?
a) 30
b) 20
c) 58
d) 48
e) 38
Explanation:
Let the numbers be X, Y and Z. Then,
X + Y + Z = 98, X/Y = 2/3 and Y/Z = 5/8
Therefore, X = 2Y/3 and Z = 8Y/5. So, 2Y/3 + Y + 8Y/5 = 98.
49Y/15 = 98
Y = 30.

9. The average weight of 8 sailors in a boat is increased by 1 kg if one of them weighing 56 kg is replaced by a new sailor. The weight of the new sailor is?
a) 57 kg
b) 60 kg
c) 64 kg
d) 62 kg
e) 68 kg
Explanation:
The sailor weighing 56 kg is replaced and the average is increased by 1 kg.
Hence, the weight of the new sailor is (56 + increase in total weight)
= 56 +1 x 8
= 56 + 8 = 64 kg.

10. A number X equals 80% of the average of 5, 7, 14 and a number Y. If the average of X and Y is 26, the value of Y is?
a) 13
b) 26
c) 39
d) Can’t be determined
e) None of these