Average


  1. The average of nine numbers is 50. The average of the first five numbers is 54 and that of the last three numbers is 52. Then the sixth number is









  1. View Hint View Answer Discuss in Forum

    Given , Sum of 9 numbers = 9 × 50 = 450
    Sum of the first 5 numbers = 5 × 54 = 270
    and Sum of the last 3 numbers = 3 × 52 = 156
    ∴ The sixth number = Sum of 9 numbers - Sum of the first 5 numbers - Sum of the last 3 numbers

    Correct Option: C

    Given , Sum of 9 numbers = 9 × 50 = 450
    Sum of the first 5 numbers = 5 × 54 = 270
    and Sum of the last 3 numbers = 3 × 52 = 156
    ∴ The sixth number = Sum of 9 numbers - Sum of the first 5 numbers - Sum of the last 3 numbers
    The sixth number = 450 – 270 – 156 = 24


  1. Out of four numbers, the average of the first three is 15 and that of the last three is 16. If the last number is 19, the first is









  1. View Hint View Answer Discuss in Forum

    Given , Sum of first 3 numbers = 15 × 3 = 45
    ⇒ a + b + c = 45 ,
    last number = d = 19
    and Sum of the last three numbers = 16 × 3 = 48
    ⇒ b + c + d = 48
    ⇒ b + c = 48 – 19 = 29

    Correct Option: C

    Given , Sum of first 3 numbers = 15 × 3 = 45
    ⇒ a + b + c = 45 ,
    last number = d = 19
    and Sum of the last three numbers = 16 × 3 = 48
    ⇒ b + c + d = 48
    ⇒ b + c = 48 – 19 = 29
    ∴ a + b + c = 45
    ⇒ a = 45 – 29 = 16



  1. The mean of 11 numbers is 35. If the mean of first 6 numbers is 32 and that of the last 6 numbers is 37, find the sixth number.









  1. View Hint View Answer Discuss in Forum

    Given , Sum of 11 numbers = 35 × 11 = 385
    Sum of the first 6 numbers = 32 × 6 = 192
    and Sum of the next 9 numbers = 37 × 6 = 222
    ∴ Sixth number = Sum of the first 6 numbers + Sum of the last 6 numbers – Sum of 11 numbers

    Correct Option: B

    Given , Sum of 11 numbers = 35 × 11 = 385
    Sum of the first 6 numbers = 32 × 6 = 192
    and Sum of the next 9 numbers = 37 × 6 = 222
    ∴ Sixth number = Sum of the first 6 numbers + Sum of the last 6 numbers – Sum of 11 numbers
    Sixth number= 192 + 222 – 385 = 29


  1. Out of four numbers, the average of the first three is 18 and that of the last three is 16. If the last number is 19, the first is









  1. View Hint View Answer Discuss in Forum

    Here , Sum of first three = 18 × 3
    ⇒ a + b + c = 54
    and Sum of last three = 16 × 3
    ⇒ b + c + d = 48
    last number = 19
    ∴ a + b + c – b – c – d
    ⇒ 54 – 48 = 6

    Correct Option: D

    Here , Sum of first three = 18 × 3
    ⇒ a + b + c = 54
    and Sum of last three = 16 × 3
    ⇒ b + c + d = 48
    last number = 19
    ∴ a + b + c – b – c – d
    ⇒ 54 – 48 = 6
    ⇒ a – d = 6
    ⇒ a – 19 = 6
    ⇒ a = 19 + 6 = 25



  1. The average of three numbers is 135. The largest number is 195 and the difference between the other two is 20. The smallest number is









  1. View Hint View Answer Discuss in Forum

    According to the question,
    Sum of numbers = Average × Total number of terms
    195 + y + ( y + 20 ) = 135 × 3
    ⇒ 2y + 215 = 405
    ⇒ 2y = 405 – 215 = 190

    Correct Option: B

    According to the question,
    Sum of numbers = Average × Total number of terms
    195 + y + ( y + 20 ) = 135 × 3
    ⇒ 2y + 215 = 405
    ⇒ 2y = 405 – 215 = 190

    ∴ y =
    190
    = 95
    2

    Required Smallest number is 95.