Dear Reader,
Below are 4 questions on averages to practice for CTS and other similar company papers.
Question 1
A group of students from Netherlands visited Chennai to study about the various aspects of life prevalent in Chennai. They also studied about the weather forecasts. The average temperature of days from Sunday to Wednesday was 36 degrees and that of from Monday to Thursday was 33.5 degrees, The temperature on Thursday was 2/3 of Sunday. What was the temperature on Sunday?
a) 20 b) 30 c) 40 d) 38
Answer : b) 30 degrees
Solution :
Average Temperature from Sunday to Wednesday - 36.
Total temperature from Sunday to Wednesday - 36 x 4 = 144 deg.
Average temperature from Monday to Thursday – 33.5 deg.
Total temperature from Monday to Thursday - 33.5 x 4 = 134
If the total temperature from Monday to Wednesday be K
Then, Sunday’s temperature + K = 144 -> eq 1
Thursday’s temperature + K = 134 -> eq 2
It is stated that Thursday temperature was 2/3 of Sunday. Applying this to eq 2, we get :
2/3 (Sunday’s Temperature) + K = 134 -> eq 3
Eq 1 – Eq 3 => 1/3 (Sunday’s Temperature) = 10. Therefore, Sunday temperature = 30 deg.
Question 2
A prominent School in Chennai had classes from LKG to XII standard. A study was made about the marks scored by students of XII in a government examination. The average marks of 60 students in a class was 45. The average marks of the boys in the class is 40 and the average marks of the girls in the class is 50. What is the ratio between the number of boys and girls in the class?
a) 1: 1 b) 2 : 1 c) 3 : 1 d) none of these.
Answer : a) 1 : 1
Solution :
Total marks of 60 students = 60 x 45 = 2700
Suppose number of girls = x
Number of boys = (60 - x)
Number of girls X average marks of girls + Number of boys x average marks of boys = 2700
x X 50 + (60 - x) 40 = 2700
50x + 2400 – 40x = 2700
By simplifying we get x = 30. Number of boys = 30 . Number of girls = 60 – x = 60 – 30 = 30
Therefore ratio of number of boys to girls = 30 / 30 = 1
Question 3
The average number of visitors to a museum from Wednesday to Saturday was 2345. Average number of visitors to it from Thursday to next Sunday was 2100. If the number of visitors to the museum on Sunday was 1820, find the number of visitors to the museum on Wednesday.
a) 2700 b) 2900 c) 2400 d) 2800
Answer : d) 2800.
Solution :
The average no. of of visitors from Wednesday to Saturday – 2345
Total number of visitors from Wednesday to Saturday - 2345 x 4 = 9380
Average number of visitors from Thursday to Sunday - 2100
Total number of visitors from Thursday to Sunday - 2100 x 4 = 8400
Number of visitors on Sunday - 1820.
So number of visitors from Thursday to Saturday - 8400 - 1820 = 6580
But it is given that, Number of visitors from Wednesday to Saturday - 9380
Therefore, Number of visitors on Wednesday = 9380 - 6580 = 2800
Question 4
A prominent School at Siliguri had three batches of students numbering 35,40 and 50 respectively. The average marks of these batches is 40, 45 and 55 respectively. What is the average mark of all the three batches students put together?
a) 48.6 b) 49.6 c) 51 d) 47.6
Answer : d) 47.6
Solution :
Total marks of all 3 batches = Number of students in I batch x Average of I batch + Number of students in II batch x Average of I batch + Number of students in I batch x Average of I batch = [ (35 x 40) + (40 x 45) + (50 x 55)]
Total number of students in all III batches = 35 + 40 + 50 = 125
Average marks of all students of III batches = Total marks of all 3 batches / Total number of students.
= [ (35 x 40) + (40 x 45) + (50 x 55)] divided by 125 = 47.6