Aptitude : Problems on Average

(6) The average weight of a class of 25 students is 45 kg. If the weight of the teacher is included, the average weight increases by 200 g. What is the weight of the teacher?

• (a)55.5 kg
• (b)60.25 kg
• (c)50.2 kg
• (d)65.55 kg

Answer

Correct Answer : (c) 50.2 kg
First, let’s convert the increased average weight to the same units as the original average weight, i.e., kilograms. An increase of 200 grams is equivalent to 0.2 kg.
So, the new average weight, when the teacher’s weight is included, is 45.2 kg.
This new average is for 26 individuals (25 students + 1 teacher).
The total weight of these 26 individuals is therefore 45.2 kg * 26 = 1175.2 kg.
However, we know that the total weight of the 25 students alone is 45 kg * 25 = 1125 kg.
To find the teacher’s weight, we subtract the total weight of the students from the total weight of the class (including the teacher).
So, the teacher’s weight is 1175.2 kg – 1125 kg = 50.2 kg.

(7) The average marks of a student in 5 subjects is 85. If his average marks in 4 subjects is 80, what are his marks in the 5th subject?

• (a)105
• (b)110
• (c)115
• (d)120

Answer

Correct Answer : (a) 105
The average marks of the student in 5 subjects is 85. So, the total marks in these 5 subjects would be 85 * 5 = 425.
The average marks in 4 subjects is 80. Therefore, the total marks in these 4 subjects is 80 * 4 = 320.
To find the marks in the 5th subject, we subtract the total marks of the 4 subjects from the total marks of all 5 subjects. So, the marks in the 5th subject would be 425 – 320 = 105.

(8) The average temperature from Monday to Wednesday was 37 degrees and from Tuesday to Thursday was 34 degrees. If the temperature on Thursday was 4/5th of Monday, what was the temperature on Thursday?

• (a)37 degrees
• (b)36 degrees
• (c)35.5 degrees
• (d)70 degrees

Answer

Correct Answer : (b) 36 degrees
Let’s denote the temperature on Monday as M, Tuesday as T, and Wednesday as W. The problem states:
The average temperature from Monday to Wednesday (M + T + W) / 3 = 37
The average temperature from Tuesday to Thursday (T + W + Th) / 3 = 34
From the first equation, we can say M + T + W = 37 * 3 = 111
From the second equation, we can say T + W + Th = 34 * 3 = 102
The problem also states that the temperature on Thursday was 4/5th of Monday. So, Th = 4/5 * M
We have three equations here, but we only need to find the value of Th. Here’s how we can do it:
Subtract the second equation from the first to get M – Th = 111 – 102 = 9
We know that Th = 4/5 * M, so we can substitute Th in the equation above:
M – 4/5 * M = 9
Solving this gives M = 45
Substituting M = 45 in the equation Th = 4/5 * M, we get Th = 4/5 * 45 = 36
So, the temperature on Thursday was 36 degrees.

(9) The average score of a cricketer for ten matches is 38.9 runs. If the average for the first six matches is 42, what is the average for the last four matches?

• (a)32.5 runs per match
• (b)33.5 runs per match
• (c)36.5 runs per match
• (d)34.25 runs per match

Answer

Correct Answer : (d) 34.25 runs per match
The total runs scored by the cricketer in ten matches is the average times the number of matches, or 38.9 runs/match * 10 matches = 389 runs.
The total runs scored in the first six matches is the average times the number of matches, or 42 runs/match * 6 matches = 252 runs.
So the total runs scored in the last four matches is the total runs minus the runs scored in the first six matches, or 389 runs – 252 runs = 137 runs.
Therefore, the average score for the last four matches is the total runs in those matches divided by the number of matches, or 137 runs / 4 matches = 34.25 runs/match.

(10) A car travels at an average speed of 60 km/h for the first half of the journey and at an average speed of 80 km/h for the second half. What is the average speed for the whole journey?

• (a)68.57 km/h
• (b)70.5 km/h
• (c)58.5 km/h
• (d)75.5 km/h

Answer

Correct Answer : (a) 68.57 km/h
When you are given average speeds for different parts of a journey, and those parts are described as fractions of the total distance (as in this case, where you have average speeds for the first half and the second half of the journey), the overall average speed can’t be calculated by simply averaging the two given speeds.
However, the harmonic mean can be used when the total distance is divided into two equal parts and we have different speeds for each part.
The formula for the harmonic mean for 2 numbers (a and b) is given by:
Harmonic Mean = 2ab / (a+b)
In this case, we have two speeds: 60 km/h for the first half and 80 km/h for the second half.
So, the average speed for the whole journey is:
Average Speed = 26080 / (60 + 80) = 9600 / 140 = 68.57 km/h
NOTE : Here “half” refers to the distance, not the time. This is why we need to use the harmonic mean to find the average speed.