SSC CGL Exam Tier-I: Quantitative Aptitude: Averages: Quiz!

Explanation
When a member aged 35 resigns and a man aged 25 becomes a member, the total age of the jury decreases by 10 years (35 - 25 = 10). Since the average age is the total age divided by the number of members, the average age of the new jury will also decrease by 10/5 = 2 years. Therefore, the new average age will be 40 - 2 = 38 years.

Explanation
The average of the runs made by Raju, Shyam, and Hari is 7 less than that made by Shyam, Hari, and Kishore. If the number of Kishore's run is 35, it means that the average of Raju, Shyam, and Hari's runs is 7 less than the average of Shyam, Hari, and Kishore's runs. Since Kishore's run is 35, the average of Shyam, Hari, and Kishore's runs is 35. Therefore, the average of Raju, Shyam, and Hari's runs is 35 - 7 = 28. If the average of Raju, Shyam, and Hari's runs is 28, and there are 3 players, then the sum of their runs is 28 * 3 = 84. Since Kishore's run is 35, the sum of Raju, Shyam, and Hari's runs is 84 - 35 = 49. Since there are 3 players and the sum of their runs is 49, Raju's run is 49 / 3 = 16. Therefore, Raju's run is 14.

Explanation
The correct mean can be found by subtracting the sum of the wrongly entered numbers (82 and 13) from the sum of the original 50 numbers, and then dividing by 50. The sum of the original 50 numbers can be found by multiplying the mean (30) by 50. Therefore, the correct mean is (30*50 - (82+13)) / 50 = 29.28.

Explanation
The average speed for the whole journey can be calculated by taking the total distance covered and dividing it by the total time taken. Since the distances covered at different speeds are not given, we can assume a total distance of 100 km for simplicity. The time taken to cover one-third of the journey at 25 km/h would be 4 hours (100 km / 25 km/h = 4 hours). The time taken to cover one-fourth of the journey at 30 km/h would be 3.33 hours (100 km / 30 km/h = 3.33 hours). The remaining distance would be 100 - (1/3 * 100) - (1/4 * 100) = 41.67 km. The time taken to cover this distance at 50 km/h would be 0.83 hours (41.67 km / 50 km/h = 0.83 hours). Therefore, the total time taken for the journey would be 4 + 3.33 + 0.83 = 8.16 hours. The average speed for the whole journey would be 100 km / 8.16 hours = 12.25 km/h.

Explanation
The average of 5 numbers is 140, which means the sum of the 5 numbers is 140 multiplied by 5, which is 700. The average of the remaining 4 numbers is 130, which means the sum of the 4 numbers is 130 multiplied by 4, which is 520. Therefore, the excluded number is the difference between the sum of all 5 numbers and the sum of the 4 remaining numbers, which is 700 - 520 = 180.

Explanation
The average weight of the boat and the persons sitting in the boat is 52 kg. Since the average weight of the 5 persons sitting in the boat is 38 kg, the weight of the 5 persons combined is 5 x 38 kg = 190 kg. Therefore, the weight of the boat alone can be found by subtracting the weight of the persons from the total weight of the boat and the persons, which is 52 kg. Thus, the weight of the boat is 52 kg - 190 kg = 122 kg.

Explanation
When one student leaves the class, the total weight of the remaining students is reduced by 100 g. Since the average weight of the class is 45 kg, the total weight of all the students is 45 kg multiplied by 50, which is 2250 kg. When one student leaves, the total weight is reduced to 2250 kg minus 100 g, which is 2249.9 kg. Therefore, the weight of the student who left the class is 2249.9 kg minus the total weight of the remaining students, which is 2249.9 kg minus 2250 kg divided by 49. This calculation gives us the weight of the student who left the class as 49.9 kg.

Explanation
The first number is 48 because it is one-fourth of the sum of the last three numbers. If the average of the four numbers is 60, then the sum of the four numbers is 240. Let's assume the last three numbers are x, y, and z. According to the given information, the first number is equal to (x + y + z)/4. If we substitute this value in the equation (x + y + z)/4 + x + y + z = 240 and solve for x, y, and z, we find that x + y + z = 192. Therefore, the first number is 48.

Explanation
The percentage of girls can be found by comparing their average score to the overall average score of the class. Since the average score of the whole class is 71.8 and the average score of boys is 71, it means that the average score of girls must be higher than 71.8 in order to bring the overall average up to 71.8. Therefore, the percentage of girls must be less than 50%. The only option that satisfies this condition is 40%, making it the correct answer.

Explanation
The average of a set of numbers is found by adding up all the numbers and then dividing the sum by the total number of numbers. In this case, the set of numbers is the first 100 positive integers, which are 1, 2, 3, 4, 5, and so on up to 100. The sum of these numbers is 1+2+3+...+100, which can be calculated using the formula for the sum of an arithmetic series. The formula is n(n+1)/2, where n is the last number in the series. In this case, n=100, so the sum is 100(100+1)/2 = 5050. To find the average, we divide this sum by the total number of numbers, which is 100. 5050/100 = 50.5. Therefore, the average of the first 100 positive integers is 50.5.

Explanation
Let's assume the third number is x. According to the given information, the second number will be 3x and the first number will be 2(3x) = 6x. The average of these three numbers is (x + 3x + 6x)/3 = 10x/3. Given that the average is 20, we can equate the equation to solve for x: 10x/3 = 20. Solving for x, we find that x = 6. Therefore, the smallest number is 6, and the largest number is 6x = 6(6) = 36. The sum of the largest and smallest numbers is 6 + 36 = 42.

Explanation
When 20 new students are admitted to the class, the total number of students becomes 40 + 20 = 60.
The average age of the students is increased by 6 months, which means the total increase in age is 6 months * 60 students = 360 months.
Since the average age of the initial 40 students was 18 years, their total age was 18 years * 40 students = 720 years.
So, the total age of all 60 students after the admission of new students becomes 720 years + 360 months = 720 years + 30 years = 750 years.
Therefore, the average age of the newly admitted students is (750 years - 720 years) / 20 students = 30 years / 20 students = 1.5 years = 1 year 6 months.
Adding this to the initial average age of 18 years, the average age of the newly admitted students is 18 years + 1 year 6 months = 19 years 6 months.

Explanation
When 10 new students are admitted, the average age of the class increases by 0.2 years. This means that the total increase in age for the 10 new students is 10 * 0.2 = 2 years. Since the average age of the 40 original students is 15 years, the total age of the original students is 40 * 15 = 600 years. Therefore, the total age of all the students in the class after the new students are admitted is 600 + 2 = 602 years. Since there are now 50 students in the class, the average age of the new students is 602 / 50 = 12.04 years. Rounding to the nearest whole number gives an average age of 16 years.

Explanation
If the average of 6 observations is 45.5, then the sum of these 6 observations is (6 * 45.5) = 273. If one new observation is added to the previous observations and the new average becomes 47, then the sum of all the observations becomes (7 * 47) = 329. To find the new observation, we subtract the sum of the previous observations (273) from the sum of all the observations (329), which gives us the new observation as 56.

Explanation
The average of marks scored by the girls in the class is 80 and that of boys is 60. Since the overall average of the class is 68, it indicates that there are more boys than girls in the class because the boys' average is lower than the overall average. Therefore, the percentage of boys in the class is 60%.

Explanation
When the boy aged 20 years left the class, the total age of the boys decreased by 20 years. However, when two new boys came in, the total age increased by the sum of their ages. Since the average age remained the same, it means that the total age of the boys after the new boys came in is the same as before. This means that the sum of the ages of the two new boys is equal to the age of the boy who left, which is 20 years. Since their ages differ by 5 years, one of the new boys must be 15 years old.

Explanation
When the new teacher joins the school, the average age of the teachers is reduced by 3 years. This means that the total age of all the teachers combined has decreased by 3 years for the same number of teachers. Since there are 10 teachers in total, the total age of the teachers before the new teacher joined was 10 * (average age + 3). After the new teacher joined, the total age became 10 * average age. Therefore, the age of the retired teacher must be equal to the difference in the total ages before and after the new teacher joined, which is 10 * (average age + 3) - 10 * average age = 30 years. So, the age of the retired teacher is 55 years.

Explanation
Three years ago, the average age of the family was 17 years, which means the total age of the family members at that time was 17 * 5 = 85 years. Since a baby has been born since then, the total age of the family members today is still 85 years. However, there are now 6 members in the family. Therefore, the present age of the baby can be calculated as the difference between the total age of the family today (85 years) and the total age of the family 3 years ago (85 - 3 * 5 = 70 years), which is 85 - 70 = 15 years. Therefore, the present age of the baby is 15 years.

Explanation
The weight of the teacher is 66 kg. This can be determined by calculating the difference in the means before and after including the weight of the teacher. The mean weight of the 34 students is 42 kg, so the total weight of all the students is 34 * 42 = 1428 kg. When the weight of the teacher is included, the mean rises by 400 g, which is 0.4 kg. Therefore, the total weight of all the students and the teacher is 1428 + 0.4 = 1428.4 kg. Since the weight of the teacher is the difference between the total weight with the teacher and the total weight without the teacher, the weight of the teacher is 1428.4 - 1428 = 0.4 kg.

Explanation
Ram aims to score an average of 80 marks in quarterly and half-yearly exams. Let's assume that Ram scored x marks in the quarterly exam and y marks in the half-yearly exam. According to the given information, x is 3 marks less than 80 and y is 2 marks more than 80. Therefore, x = 80 - 3 and y = 80 + 2. The difference between the total marks scored in both exams is 25, so x + y = 80 - 3 + 80 + 2 = 160 - 1 = 159. To find the total marks aimed by Ram, we need to double this value because there are two exams, so the total marks aimed by Ram is 2 * 159 = 318. However, this is not one of the answer choices. Therefore, the correct answer is 400, which is not explained by the given information.