Averages — Set #2 | Practice

{"setId":"28691b80-b80e-4940-929d-96bac3e5e459","setTitle":"Averages Aptitude Quiz 2– UPSC CSAT","topicName":"Averages","topicSlug":"averages","setNumber":2,"totalQuestions":10,"questions":[{"id":"4d5fe6a0-d50b-4d9f-b75b-cbfb3f486730","order":1,"statement":"Which of the following is the smallest of four consecutive even numbers if their average is 57?","options":{"A":"52","B":"54","C":"56","D":"58"},"correctOption":"B","solution":"Let the numbers be x, (x+2), (x+4), (x+6). Their average = [x+(x+2)+(x+4)+(x+6)]/4 = (4x+12)/4 = x+3 = 57, so x = 54. The numbers are 54, 56, 58, 60, making 54 the smallest."},{"id":"b90c364f-9391-404b-a3e8-ad8719b5c110","order":2,"statement":"What is the mean of the initial 70 natural numbers?","options":{"A":"35.5","B":"35.3","C":"35.1","D":"35"},"correctOption":"A","solution":"Sum of first n natural numbers = n(n+1)/2. Sum of 70 natural numbers = 70×71/2 = 2485. Mean = 2485/70 = 35.5."},{"id":"b4e0e35b-9017-4d46-9036-367ad2e37c30","order":3,"statement":"In a house, there are three siblings: two sisters and one brother, along with their parents. The average weight of the sisters and their mother is 60 kg. The average weight of the brother and his father is 70 kg. If the weight of the father is 80 kg and the weight of the brother is equal to that of two sisters, then what is the weight of the mother?","options":{"A":"70 kg","B":"80 kg","C":"100 kg","D":"120 kg"},"correctOption":"D","solution":"Let brother's weight = x kg. Average of brother and father = (x+80)/2 = 70, so x = 140-80 = 60 kg. This is the weight of the brother, which equals the combined weight of the two sisters (60 kg). Weight of mother = (Total weight of sisters and mother) - (Total weight of two sisters) = 60×3 - 60 = 180-60 = 120 kg."},{"id":"fcb2bf87-ee86-4698-aa40-2cac36b0bccc","order":4,"statement":"The average age of 25 students in a class is 20 years, while the average age of 15 teachers in the same school is 35 years. What is the approximate average age of all the students and teachers together?","options":{"A":"26 years","B":"23 years","C":"24 years","D":"27 years"},"correctOption":"A","solution":"Total age of students = 20×25 = 500 years. Total age of teachers = 35×15 = 525 years. Combined total age = 500+525 = 1025 years. Total number of people = 25+15 = 40. Average = 1025/40 = 25.625 ≈ 26 years."},{"id":"7d7c2256-e878-45d5-b0c5-63d3f94bba5c","order":5,"statement":"In a school, there are three sections: X, Y, and Z in class 10th. Section X has 25 students with an average height of 160 cm, Section Y has 30 students with an average height of 155 cm, and Section Z has 35 students with an average height of 150 cm. Calculate the average height of all the students in class 10th of the school.","options":{"A":"145.44 cm","B":"154.44 cm","C":"144.44 cm","D":"155.44 cm"},"correctOption":"B","solution":"Total height = 25×160 + 30×155 + 35×150 = 4000+4650+5250 = 13900 cm. Total number of students = 25+30+35 = 90. Average height = 13900/90 = 154.44 cm."},{"id":"c8d690a6-780f-4aa2-bf45-94ca8a928d78","order":6,"statement":"Ten friends decided to go to a movie theatre. Nine of them spent ₹35 each on their movie tickets, while the tenth friend decided to spend ₹10 more than the average expenditure of all ten friends. What was the total amount of money spent by them on movie tickets?","options":{"A":"₹ 360.11","B":"₹ 361.11","C":"₹ 362.11","D":"₹ 363.33"},"correctOption":"B","solution":"Let average expenditure of all ten friends = x. The tenth friend spent x+10, so total = 9×35 + (x+10) = 315+x+10. This total also equals 10x (10 friends × average x). So 10x = 315+x+10, giving 9x = 325, x = ₹36.11. Total amount spent = 315 + (36.11+10) = 315+46.11 = ₹361.11."},{"id":"bbfc9af8-5d8c-4b00-bd79-9ba156c739b9","order":7,"statement":"The average score of Aakash, Bhuvan and Chandan in class test is 85. The average score of Bhuvan, Deepak, and Ekta in the class test is 90, and the score of Fatima is equal to that of Bhuvan. What is the average score of Aakash, Bhuvan, Chandan, Deepak, Ekta, and Fatima in the test?","options":{"A":"86","B":"86.5","C":"87","D":"87.5"},"correctOption":"D","solution":"Total score of Aakash, Bhuvan, Chandan = 85×3 = 255. Total score of Bhuvan, Deepak, Ekta = 90×3 = 270. Since Fatima's score equals Bhuvan's, adding Fatima's score to (Deepak+Ekta) gives Deepak+Ekta+Fatima = 270 (since Bhuvan's score is already counted once within this 270). Total score of all six students = 255+270 = 525. Average = 525/6 = 87.5."},{"id":"69b81f6a-9cc4-4cc2-a19b-62d01d79f7bd","order":8,"statement":"In a quiz competition, there are 10 participants whose age ranges from 20 to 40 years. The average age of the participants is 30 years. If three new participants join the competition, the average age of the participants becomes 32 years. Which of the following options can be the set of the ages of the three new participants who joined the competition?","options":{"A":"42 years, 39 years, 37 years","B":"39 years, 37 years, 35 years","C":"42 years, 37 years, 37 years","D":"39 years, 37 years, 48 years"},"correctOption":"C","solution":"Sum of ages of initial 10 participants = 10×30 = 300 years. Sum of ages of all 13 participants after joining = 13×32 = 416 years. Sum of ages of the three new participants = 416-300 = 116 years. Checking option C: 42+37+37 = 116, which matches."},{"id":"2371cfa2-84f1-4898-b578-f8ac97b80243","order":9,"statement":"In a school, the average age of teachers and students is 25 years. The average age of all 30 students is 20 years, and the average age of teachers is 30 years. If 15 teachers are married, how many unmarried teachers are there in the school?","options":{"A":"15","B":"25","C":"30","D":"32"},"correctOption":"A","solution":"Let number of teachers = x. Then 30x + 30×20 = 25×(30+x), giving 30x+600 = 750+25x, so 5x = 150, x = 30. Number of married teachers = 15, so unmarried teachers = 30-15 = 15."},{"id":"76ca4117-380c-4c89-b487-e3c72da58786","order":10,"statement":"In a hostel, there were initially 45 students. When 5 new students were admitted, the daily expenses of the mess increased by Rs. 50, and as a result, the average expenditure per student decreased by Rs. 5. What was the original daily expenditure of the mess?","options":{"A":"₹ 2600","B":"₹ 2700","C":"₹ 2800","D":"₹ 2900"},"correctOption":"B","solution":"Let original average expenditure per student = x. New total expenditure (for 50 students) = 45x+50, and this also equals 50(x-5). So 50(x-5) = 45x+50, giving 50x-250 = 45x+50, so 5x = 300, x = 60. Original daily expenditure = 45×60 = ₹2700."}]}