Average
- The arithmetic mean of the following numbers
1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6 and 7, 7, 7, 7, 7, 7, 7 is
-
View Hint View Answer Discuss in Forum
Required mean = 1 × 1 + 2 × 2 + 3 × 3 + 4 × 4 + 5 × 5 + 6 × 6 + 7 × 7 1 + 2 + 3 + 4 + 5 + 6 + 7 Required mean = 1 + 4 + 9 + 16 + 25 + 36 + 49 1 + 2 + 3 + 4 + 5 + 6 + 7
Correct Option: B
Required mean = 1 × 1 + 2 × 2 + 3 × 3 + 4 × 4 + 5 × 5 + 6 × 6 + 7 × 7 1 + 2 + 3 + 4 + 5 + 6 + 7 Required mean = 1 + 4 + 9 + 16 + 25 + 36 + 49 1 + 2 + 3 + 4 + 5 + 6 + 7 Required mean = 140 28
Required mean = 5
- There are 100 students in 3 sections A, B and C of a class. The average marks of all the 3 sections was 84. The average of B and C was 87.5 and the average marks of A is 70. The number of students in A was
-
View Hint View Answer Discuss in Forum
Number of students in section A = n
∴ Number of students in sections B and C = (100 – n)
∴ n × 70 + (100 – n) × 87.5 = 84 × 100
⇒ 70n + 87.5 × 100 – 87.5n = 8400
⇒ 8750 – 17.5n = 8400
⇒ 17.5n = 8750 – 8400 = 350Correct Option: C
Number of students in section A = n
∴ Number of students in sections B and C = (100 – n)
∴ n × 70 + (100 – n) × 87.5 = 84 × 100
⇒ 70n + 87.5 × 100 – 87.5n = 8400
⇒ 8750 – 17.5n = 8400
⇒ 17.5n = 8750 – 8400 = 350⇒ n = 350 = 20 17.5
- The average of 30 numbers is 15. The average of the first 18 numbers is 10 and that of the next 11 numbers is 20. The last number is
-
View Hint View Answer Discuss in Forum
The average of 30 numbers = 15
The average of the first 18 numbers = 10
and the average of next 11 numbers = 20
Let the last number be n.
According to the question,
18 × 10 + 11 × 20 + n = 30 × 15Correct Option: D
The average of 30 numbers = 15
The average of the first 18 numbers = 10
and the average of next 11 numbers = 20
Let the last number be n.
According to the question,
18 × 10 + 11 × 20 + n = 30 × 15
⇒ 180 + 220 + n = 450
⇒ 400 + n = 450
⇒ n = 450 – 400 = 50
- The average of some natural numbers is 15. If 30 is added to first number and 5 is subtracted from the last number the average becomes 17.5 then the number of natural number is
-
View Hint View Answer Discuss in Forum
Number of natural numbers = p
∴ Their sum = 15p
According to the question,
15p + 30 – 5 = p × 17.5
⇒ 17.5p – 15p = 25
⇒ 2.5p = 25Correct Option: D
Number of natural numbers = p
∴ Their sum = 15p
According to the question,
15p + 30 – 5 = p × 17.5
⇒ 17.5p – 15p = 25
⇒ 2.5p = 25
⇒ p = 25/2.5 = 10
- The average weight of 3 men A, B and C is 84 kg. Another man D joins the group and the average now becomes 80 kg. If another man E whose weight is 3 kg more then that of D, replaces A, then the average weight of B, C, D and E becomes 79 kg. Then weight of A is
-
View Hint View Answer Discuss in Forum
D’s weight = 80 × 4 – 84 × 3
D’s weight = 320 – 252 = 68 kg.
E’s weight = 68 + 3 = 71 kg.
Total weight of (A + B + C + D + E) = 84 × 3 + 68 + 71
Total weight of (A + B + C + D + E) = 252 + 68 + 71 = 391 kg.
Total weight of (B + C + D + E) = 79 × 4 = 316 kg.Correct Option: C
D’s weight = 80 × 4 – 84 × 3
D’s weight = 320 – 252 = 68 kg.
E’s weight = 68 + 3 = 71 kg.
Total weight of (A + B + C + D + E) = 84 × 3 + 68 + 71
Total weight of (A + B + C + D + E) = 252 + 68 + 71 = 391 kg.
Total weight of (B + C + D + E) = 79 × 4 = 316 kg.
∴ A’s weight = Total weight of (A + B + C + D + E) - Total weight of (B + C + D + E)
A’s weight = 391 – 316 = 75 kg.
