Averages — Set #1 | Practice

{"setId":"27864a0a-1064-4a03-985f-bcd5350c1042","setTitle":"Averages Aptitude Quiz – UPSC CSAT","topicName":"Averages","topicSlug":"averages","setNumber":1,"totalQuestions":10,"questions":[{"id":"8acfe13c-52e4-49fc-bb7d-385115a666cb","order":1,"statement":"Consider the following statements: I. The average of any 5 consecutive odd natural numbers is 'p'. If two more such numbers, just next to the previous 5 numbers are added, the new average becomes (2p+1). II. The average of 3 consecutive natural numbers (which are in increasing order) is 'p'. If two more consecutive numbers, just next to the first set of numbers, is added, then the new average becomes (p+1). Which of the statements given above are correct?","options":{"A":"I only","B":"II only","C":"Both I and II","D":"Neither I nor II"},"correctOption":"B","solution":"Statement I: The 5 consecutive odd numbers are (p-4),(p-2),p,(p+2),(p+4). Adding two more, (p+6) and (p+8), gives 7 numbers summing to 7p+14, so new average = (7p+14)/7 = p+2, not (2p+1). Statement I is incorrect. Statement II: The 3 consecutive natural numbers are (p-1),p,(p+1). Adding two more, (p+2) and (p+3), gives 5 numbers summing to 5p+5, so new average = (5p+5)/5 = p+1. Statement II is correct. Therefore, only statement II is correct."},{"id":"44e64c4a-6a9a-4fc0-9213-c9b5eb749ed8","order":2,"statement":"The average cost price of 20 pencils (having equal cost price) decreases by Rs. 2, when one of the pencils is replaced by a new pencil having cost price of Rs. 80. Find the cost price of the pencil that was replaced.","options":{"A":"Rs. 50","B":"Rs. 100","C":"Rs. 120","D":"Rs. 180"},"correctOption":"C","solution":"Let the average cost price of 20 pencils be x, so total cost = 20x. After replacement, new average = x-2, so new total cost = 20(x-2) = 20x-40. Difference between old and new total = 20x-(20x-40) = Rs. 40, meaning the replaced pencil's cost was Rs. 40 more than the new pencil's cost. Cost of new pencil = Rs. 80, so cost of replaced pencil = 80+40 = Rs. 120."},{"id":"f9aa4dc7-1877-41f6-91fe-0acd3511cad7","order":3,"statement":"The average marks obtained by 30 students in a math test is 60. The average mark of the first 15 students is 70, and those of the last 16 students is 50. What is the marks obtained by the 15th student?","options":{"A":"70","B":"60","C":"50","D":"20"},"correctOption":"C","solution":"Marks obtained by the 15th student = (Total marks of first 15 students + Total marks of last 16 students) - Total marks of all 30 students = (15×70 + 16×50) - 30×60 = (1050+800) - 1800 = 1850-1800 = 50."},{"id":"937bc7d3-d8cb-4a12-831c-7232f080ec28","order":4,"statement":"The average monthly expenses of a family consisting of 4 members amount to ₹10,000. What will be the new average monthly expenses of the family if one of the member's expenses increases by ₹5,000 per month?","options":{"A":"₹ 11,520","B":"₹ 11,205","C":"₹ 11,502","D":"₹ 11,250"},"correctOption":"D","solution":"Total monthly expenses of the family = 4×10,000 = ₹40,000. After the increase, total expenses = 40,000+5,000 = ₹45,000. New average = 45,000/4 = ₹11,250."},{"id":"62fd86e1-bb1f-4dbc-b867-38958dd4baa0","order":5,"statement":"A box contains 80 nails each of 50 grams and 90 bolts each of 75 grams. If the entire box weighs 13.25 kg, then the weight of the empty box is?","options":{"A":"2.5 kg","B":"3.25 kg","C":"4.00 kg","D":"5.75 kg"},"correctOption":"A","solution":"Total weight of nails = 80×50 = 4000 grams = 4 kg. Total weight of bolts = 90×75 = 6750 grams = 6.75 kg. Weight of empty box + 4 + 6.75 = 13.25, so weight of empty box = 13.25-10.75 = 2.5 kg."},{"id":"765c93ae-717e-49f4-a3ba-bf205c5afc94","order":6,"statement":"The average temperature in a city over 30 days was 25°C. After the next 10 days, the average temperature increased by 3.5°C. What was the average temperature in the last 10 days?","options":{"A":"22.5°C","B":"25°C","C":"28.5°C","D":"39°C"},"correctOption":"D","solution":"Total temperature for 30 days = 25×30 = 750°C. Combined average over 40 days = 25+3.5 = 28.5°C, so total temperature for 40 days = 28.5×40 = 1140°C. Total temperature for the last 10 days = 1140-750 = 390°C. Average for the last 10 days = 390/10 = 39°C."},{"id":"a6016101-d26f-4e58-a37b-1a1f9597cae0","order":7,"statement":"The average of a set of 21 numbers, is 15.5. The average of the first eleven numbers is 14.8, and that of the last eleven numbers is 16.3. What is the value of the number in the middle of the set?","options":{"A":"13.4","B":"-13.4","C":"16.6","D":"-16.6"},"correctOption":"C","solution":"Sum of 21 numbers = 15.5×21 = 325.5. Sum of first eleven numbers = 14.8×11 = 162.8. Sum of last eleven numbers = 16.3×11 = 179.3. The 11th (middle) number is counted in both groups, so: Middle number = (Sum of first eleven + Sum of last eleven) - Sum of all 21 = (162.8+179.3) - 325.5 = 342.1-325.5 = 16.6."},{"id":"33badd18-831d-4cac-9b65-b403d162f373","order":8,"statement":"In a college, there are 120 employees, and their average salary is ₹ 50,000 per year. If the average salary (per year) of male employees is ₹ 60,000, and the average salary (per year) of female employees is ₹ 45,000, then find out the number of male employees in the college.","options":{"A":"80","B":"60","C":"40","D":"20"},"correctOption":"C","solution":"Let number of male employees = a, so female employees = 120-a. Total salary equation: 120×50,000 = (120-a)×45,000 + a×60,000. This gives 60,00,000 = 54,00,000 - 45,000a + 60,000a, so 15,000a = 6,00,000, giving a = 40. Number of male employees = 40."},{"id":"d815c729-f86e-4e1c-8215-58218d2ff23b","order":9,"statement":"Six consecutive even integers are represented as 'P', 'Q', 'R', 'S', 'T' and 'U'. What is the average of these consecutive even integers?","options":{"A":"6(P+5)","B":"(P+5)","C":"(P+Q+R+S+T+U)","D":"(P+7)"},"correctOption":"B","solution":"Since P,Q,R,S,T,U are 6 consecutive even integers: Q=P+2, R=P+4, S=P+6, T=P+8, U=P+10. Average = (P+Q+R+S+T+U)/6 = [P+(P+2)+(P+4)+(P+6)+(P+8)+(P+10)]/6 = (6P+30)/6 = P+5."},{"id":"9cadcc8d-0292-4218-af73-da466e644bc1","order":10,"statement":"The average of 5 consecutive odd numbers is 49. What is the product of the smallest and the largest number?","options":{"A":"2499","B":"2385","C":"2173","D":"2279"},"correctOption":"B","solution":"For 5 consecutive odd numbers, the average equals the middle number, so the middle number is 49. The numbers are 45, 47, 49, 51, 53. Product of smallest and largest = 45×53 = 2385."}]}