Average
- The average of eight numbers is 20. If the sum of first two numbers is 31, the average of the next three numbers
is 21 1 and the seventh and eighth numbers exceed the sixth number by 4 and 7 respectively, then the eighth number is 3
-
View Hint View Answer Discuss in Forum
The average of eight numbers = 20
Sum of the eight numbers = 20 × 8 = 160
The average of first two numbers = 31
Sum of the first two numbers = 31The average of the next three numbers = 64 3 Sum of the next three numbers = 64 × 3 = 64 3
Let the sixth number = n
∴ Seventh number = n + 4
and eighth number = n + 7
Correct Option: B
The average of eight numbers = 20
Sum of the eight numbers = 20 × 8 = 160
The average of first two numbers = 31
Sum of the first two numbers = 31The average of the next three numbers = 64 3 Sum of the next three numbers = 64 × 3 = 64 3
Let the sixth number = n
∴ Seventh number = n + 4
and eighth number = n + 7
According to question ,
∴ 31 + 64 + n + n + 4 + n + 7 = 160
⇒ 3n + 106 = 160
⇒ 3n = 160 – 106 = 54
⇒ n = 54 ÷ 3 = 18
∴ Eighth number = n + 7 = 18 + 7 = 25
- The average expenditure of a man for the first five months of a year is ₹5,000 and for the next seven months it is ₹5,400. He saves ₹2,300 during the year. His average monthly income is :
-
View Hint View Answer Discuss in Forum
The average expenditure of a man for the first five months = ₹5,000
Total expenditure for 5 months = 5 × 5000
and the average expenditure of a man for the next seven months = ₹5,400
Total expenditure for next 7 months = 7 × 5400
Annual expenditure of the man = ₹(5 × 5000 + 7 × 5400)
Annual expenditure of the man = ₹(25000 + 37800) = 62800
Annual savings = ₹2300∴ Average monthly income = ₹ 
62800 + 2300 
12
Correct Option: A
The average expenditure of a man for the first five months = ₹5,000
Total expenditure for 5 months = 5 × 5000
and the average expenditure of a man for the next seven months = ₹5,400
Total expenditure for next 7 months = 7 × 5400
Annual expenditure of the man = ₹(5 × 5000 + 7 × 5400)
Annual expenditure of the man = ₹(25000 + 37800) = 62800
Annual savings = ₹2300∴ Average monthly income = ₹ 62800 + 2300 12 Average monthly income = ₹ 65100 = ₹5425 12
- The average of the three numbers x, y and z is 45. x is greater than the average of y and z by 9. The average of y and z is greater than y by 2. Then the difference of x and zis
-
View Hint View Answer Discuss in Forum
The average of the three numbers x, y and z = 45.
⇒ x + y + z = 3 × 45 = 135 ...(i)x = y + z + 9 2
⇒ 2x – y – z = 18 ...(ii)and, y + z = y + 2 2
⇒ y + z = 2y + 4
⇒ z – y = 7 ...(iii)
By equations (i) + (ii),
3x = 135 + 18 = 153
⇒ x = 51
Correct Option: C
The average of the three numbers x, y and z = 45.
⇒ x + y + z = 3 × 45 = 135 ...(i)x = y + z + 9 2
⇒ 2x – y – z = 18 ...(ii)and, y + z = y + 2 2
⇒ y + z = 2y + 4
⇒ z – y = 7 ...(iii)
By equations (i) + (ii),
3x = 135 + 18 = 153
⇒ x = 51
By equations (i) and (iii),
x + y + z + z – y = 135 + 4 = 139
⇒ x + 2z = 139
⇒ 51 + 2z = 139
⇒ 2z = 139 – 51 = 88
⇒ z = 44
∴ x – z = 51 – 44 = 7
- If the average of m numbers is n2 and that of n numbers is m2,then average of (m + n) numbers is
-
View Hint View Answer Discuss in Forum
The average of m numbers = n2
Total number of ‘m’ numbers = m × n²
And the average of n numbers = m2
Total number of ‘n’ numbers = n × m²Correct Option: C
The average of m numbers = n2
Total number of ‘m’ numbers = m × n²
And the average of n numbers = m2
Total number of ‘n’ numbers = n × m²∴ Average of (m + n) numbers = mn² + m²n = mn(n + m) = mn m + n m + n
- The average score of a-class of boys and girls in an examination is A. The ratio of boys and girls in the class is 3 : 1. If the average score of the boys is A + 1, the average score of the girls is
-
View Hint View Answer Discuss in Forum
Let the number of boys in the class be 3k. The ratio of boys and girls in the class is 3 : 1, then the number of girls in the class is k.
∴ Average score of the girls = (3k + k) × A - 3k(A + 1) k Average score of the girls = 4kA - 3kA -3k k
Correct Option: D
Let the number of boys in the class be 3k. The ratio of boys and girls in the class is 3 : 1, then the number of girls in the class is k.
∴ Average score of the girls = (3k + k) × A - 3k(A + 1) k Average score of the girls = 4kA - 3kA -3k k Average score of the girls = kA - 3k = k(A - 3) = A - 3 k k
