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Average Test 21
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Average Test 21
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  • Question 1/10
    1 / -0

    The arithmetic mean of the scores of a group of students in a test was 52. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of remaining 55% is:

    Solutions

    Explanation – Let the required mean score be a

    Then, 20 x 80 + 25 x 31 + 55 x a = 52 x 100

    1600 + 775 + 55a = 5200

    55a = 2825

    a = 51.4

     

  • Question 2/10
    1 / -0

    The average of a non-zero number and its square is 5 times the number. The number is:

    Solutions

    Explanation – Let the number be x.

    Then,

    (x + x^2) / 2 = 5x

    x^2 – 9x = 0

    x (x – 9) = 0

    x = 0 or x = 9.

     

  • Question 3/10
    1 / -0

    If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of a^2, b^2, c^2 is:

    Solutions

    Explanation –

    We have :

    (a + b + c) / 3 = M or (a + b + c) = 3M.

    Now, (a + b + c)^2 = (3M)^2 = 9M^2

    a^2 + b^2 + c^2 + 2 (ab + bc + ca) = 9M^2

    a^2 + b^2 + c^2 = 9M^2

    Required mean =

    (a^2 + b^2 + c^2)/3= 9M^2/ 3 = 3 M^ 2

     

  • Question 4/10
    1 / -0

    The average weight of 8 persons increases by 2.5 kg when a new person comes in place of one them weighing 65 kg. What might be the weight of the new person?

    Solutions

    Explanation –

    Total weight increased = (8 x 2.5) kg = 20 kg

    Weight of new person = (65 + 20) kg = 85 kg

     

  • Question 5/10
    1 / -0

    The average age of the boys in a class is 16 years and that of the girls is 15 years. The average age for the whole class is:

    Solutions

    Explanation –

    Clearly, to find the average, we ought to know the number of boys, girls or students in the class, neither of which has been given
    So, the data provided is inadequate

     

  • Question 6/10
    1 / -0

    A cricketer has completed 10 innings and his average is 21.5 runs. How many runs must he make in his next innings so as to raise his average to 24?

    Solutions

    Explanation – Total of 10 innings = 21.5 x 10 = 215

    Suppose he needs a score of a in 11th innings; then average in 11 innings =

    (215 + a) / 11= 24

    or, a = 264-215 = 49

     

  • Question 7/10
    1 / -0

    1/3 rd of certain journey is covered at the rate of 25 km/hr, 1/4 th at the rate of 30 km/hr and rest at 50 km/hr. Find the averae speed for the whole journey?

    Solutions

    Explanation – Let the journey by a km. Then a/3 km at the speed of 25 km/hr and a/4 km at 30 km/hr and the rest distance ( a- a/3 –a/4 ) = 5/12 x a at the speed of 50 km/hr.

    Total time taken during the journey of a km

     

  • Question 8/10
    1 / -0

    The average of six numbers is 3.95. The average of two of them is 3.4, while the average of the other two is 3.85. What is the average of the remaining two numbers?

    Solutions

    Explanation – Sum of the remaining two numbers = (3.95 x 6) – [(3.4 x 2) + (3.85 x 2)] = 23.70 – (6.8 + 7.7) = 23.70 – 14.5 = 9.20

    Average = 9.2/2 = 4.6

     

  • Question 9/10
    1 / -0

    The average salary of the entire staff in a office is Rs 120 per month. The average salary of officers is Rs 460 and that of non officer is Rs 110. If the number of officer is 15, then find the number of non-officer in the office?

    Solutions

    Explanation – Let the required number of non-officers = a

    Then, 110a + 460 x 15 = 120 (15 + a)

    or, 120a – 110a = 450 x 15 – 120 x 15 = 15 (460 – 120)

    or, 10a = 15 x 340; a = 15 x 34 = 510

     

  • Question 10/10
    1 / -0

    Find the average of first 20 multiple of 7?

    Solutions

    Explanation –

    Average = 7 (1+2+3+…….+20)/ 20= 7 x 20 x 21/ 20×2= 73.5

     

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