2️⃣ The average of 3 numbers is 15. If two of the numbers are 12 and 18, what is the third number?
Step-by-Step Explanation
Total sum of 3 numbers = 15 * 3 = 45.
Sum of two numbers = 12 + 18 = 30.
Third number = Total sum - Sum of two numbers.
Third number = 45 - 30 = 15.
Answer: 15 ✅
3️⃣ The average of 4 consecutive even numbers is 27. What is the smallest number?
Step-by-Step Explanation
Let the numbers be x, x+2, x+4, x+6.
Average = (x + x+2 + x+4 + x+6) / 4 = 27.
(4x + 12) / 4 = 27.
4x + 12 = 108.
4x = 96.
x = 24.
Smallest number = 24.
Answer: 24 ✅
4️⃣ The average age of 6 boys is 12 years. If one boy of age 14 years leaves, what is the average age of the remaining boys?
Step-by-Step Explanation
Total age of 6 boys = 6 * 12 = 72 years.
Age of boy leaving = 14 years.
Total age of remaining 5 boys = 72 - 14 = 58 years.
Average age of remaining 5 boys = 58 / 5 = 11.6 years.
Answer: 11.6 years ✅
5️⃣ The average weight of a group of 10 people increases by 1.5 kg when a person weighing 60 kg is replaced by a new person. What is the weight of the new person?
Step-by-Step Explanation
Total increase in weight = 10 people * 1.5 kg = 15 kg.
Weight of replaced person = 60 kg.
Weight of new person = 60 kg + 15 kg = 75 kg.
Answer: 75 kg ✅
6️⃣ The average of 5 consecutive odd numbers is 35. What is the product of the smallest and largest numbers?
Step-by-Step Explanation
Let the numbers be x, x+2, x+4, x+6, x+8.
Average = (5x + 20) / 5 = 35.
5x + 20 = 175.
5x = 155.
x = 31.
Smallest number = 31.
Largest number = 31 + 8 = 39.
Product = 31 * 39 = 1209.
Answer: 1209 ✅
7️⃣ The average marks of 30 students is 60. If the average marks of the top 10 students are 70 and the average marks of the bottom 10 students are 50, what are the average marks of the remaining 10 students?
Step-by-Step Explanation
Total marks of 30 students = 30 * 60 = 1800.
Total marks of top 10 students = 10 * 70 = 700.
Total marks of bottom 10 students = 10 * 50 = 500.
Total marks of remaining 10 students = 1800 - 700 - 500 = 600.
Average marks of remaining 10 students = 600 / 10 = 60.
Answer: 60 ✅
8️⃣ A batsman has an average score of 50 runs after 10 innings. In the 11th inning, he scores 80 runs. What is his new average?
Step-by-Step Explanation
Total runs after 10 innings = 10 * 50 = 500.
Total runs after 11 innings = 500 + 80 = 580.
New average = 580 / 11 = 52.7272...
Approximately 52.73.
Answer: 52.73 ✅
9️⃣ The average age of a group of 15 people is 35 years. If 5 people with an average age of 40 years leave the group, and 3 people with an average age of 30 years join the group, what is the new average age of the group?
Step-by-Step Explanation
Total age of 15 people = 15 * 35 = 525 years.
Total age of 5 people leaving = 5 * 40 = 200 years.
Total age of 3 people joining = 3 * 30 = 90 years.
New total age = 525 - 200 + 90 = 415 years.
New number of people = 15 - 5 + 3 = 13 people.
New average age = 415 / 13 = 31.923...
Approximately 31.92 years.
Answer: None of the provided answers are correct. The answer is approximately 31.92 years. ✅
🔟 In a class, the average score of boys is 70, and the average score of girls is 80. If the average score of the entire class is 76, what is the ratio of the number of boys to the number of girls?
Step-by-Step Explanation
Let the number of boys be 'b' and the number of girls be 'g'.