Average


  1. The average of 100 observations was calculated as 35. It was found later, that one of the observations was misread as 83 instead of 53. The correct average is :









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    According to question ,
    Difference = 83 – 53 = 30
    Incorrect observation > Correct observation

    ∴ Required average = 35 -
    30
    100

    Correct Option: B

    According to question ,
    Difference = 83 – 53 = 30
    Incorrect observation > Correct observation

    ∴ Required average = 35 -
    30
    = 35 - 0.3 = 34.7
    100


  1. The average of marks obtained by 100 candidates in a certain examination is 30. If the average marks of passed candidates is 35 and that of the failed candidates is 10, what is the number of candidates who passed the examination?









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    Number of successful students in the exam = p
    ∴ Number of unsuccessful students = 100 – p
    According to the question,

    ∴ 30 =
    35p + 10(100 - p)
    100

    ⇒ 3000 = 35p + 1000 – 10p
    ⇒ 3000 = 25p + 1000
    ⇒ 25p = 3000 – 1000 = 2000

    Correct Option: C

    According to the question,

    ∴ 30 =
    35p + 10(100 - p)
    100

    ⇒ 3000 = 35p + 1000 – 10p
    ⇒ 3000 = 25p + 1000
    ⇒ 25p = 3000 – 1000 = 2000
    ⇒ p =
    2000
    = 80
    25



  1. The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is :
    .









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    B’s weight = (A + B)’s weight + (B + C)’s weight – (A + B + C)’s weight
    B’s weight = (40 × 2 + 2 × 43 – 45 × 3) kg.
    B’s weight = (80 + 86 – 135) kg.

    Correct Option: A

    B’s weight = (A + B)’s weight + (B + C)’s weight – (A + B + C)’s weight
    B’s weight = (40 × 2 + 2 × 43 – 45 × 3) kg.
    B’s weight = (80 + 86 – 135) kg.
    B’s weight = 31 kg.


  1. The average of 25 results is 20. The average of first 12 results is 15 and that of the last 12 results is 18. Then, the 13th result is :









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    Here , The average of 25 results = 20.
    The average of first 12 results = 15
    and average of the last 12 results = 18.
    Value of 13th result = 25 × 20 – 12 × 15 – 12 × 18

    Correct Option: C

    Here , The average of 25 results = 20.
    The average of first 12 results = 15
    and average of the last 12 results = 18.
    Value of 13th result = 25 × 20 – 12 × 15 – 12 × 18
    Value of 13th result = 500 – 180 – 216
    Hence , Value of 13th result = 104



  1. The average marks obtained by a class of 60 students is 65. The average marks of half of the students is found to be 85. The average marks of the remaining students is









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    Let average marks of remaining 30 students be p.

    ∴ 65 =
    30 × 85 + 30 × p
    60

    ⇒ 65 × 60 = 2550 + 30p
    ⇒ 3900 = 2550 + 30p
    ⇒ 30p = 3900 – 2550 = 1350

    Correct Option: B

    Let average marks of remaining 30 students be p.

    ∴ 65 =
    30 × 85 + 30 × p
    60

    ⇒ 65 × 60 = 2550 + 30p
    ⇒ 3900 = 2550 + 30p
    ⇒ 30p = 3900 – 2550 = 1350
    ⇒ p =
    1350
    = 45
    30