46. The average of 8 numbers is 20. The average of first two numbers is 15 ½ and that of the next three is 21 ½. If the sixth number be less than the seventh and eighth numbers by 4 and 7 respectively, then the eighth number is:
a) 18
b) 22
c) 25
d) 27
47. If the arithmetic mean of seventy-five numbers is calculated, it is 35. If each number is increased by 5, then men of new numbers is:
a) 30
b) 40
c) 70
d) 90
48. The average of ten numbers is 7. If each number is multiplied by 12, then the average of the new set of numbers is:
a) 7
b) 19
c) 82
d) 84
49. Average of ten positive numbers is x. if each number is increased by 10%, then x: 9a) remains unchanged.
a) Remains unchanged
b) May decrease
c) May increase
d) Is increased by 10%
50. The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. Then corrected new mean is:
a) 35.2
b) 36.1
c) 36.5
d) 39.1
ANSWERS
46. C
47.D
48.D
49.D
50.C
SOLUTION
4
Seventh number = (x – 7) + 4 = (X – 3).
So, (2x 15 1/2) + (3 x 21 1/3) + (x – 7) +( x -3) + x = 8 x 20.
31 + 64 + (3x -10) = 160 3X = 75 x = 25.
47. A.M. of 75 numbers = 35.
Sum of 75 numbers = (75 x 5) = 2625.
Total increase = (75 x 5) =375.
Increased sum = (2625 + 375) = 3000.
Increased average = 3000 / 75 = 40.
48. Average of 10 numbers = 7.
Sum of these 10 numbers = (10 x 7) = 70.
x₁ + x₂+ …. + x₁₀ = 70.
12 x₁ + 12 x₂.. + 12X₁₀ = 840
12 x₁ + 12 x₂.. + 12X₁₀ = 840/10 = 84.
Average of new numbers is 84.
49. x₁ + x₂.. + X₁₀ = x = x₁ + x₂.. + X₁₀ = 10 x
= 110/100 x₁ + 110 /100 x₂ + …….110/100 x₁₀ = 110/100 x 10x.
= 110/100 x₁ + 110 /100x₂ + ……110/100x₁₀ / 10 =11/10x.
50. Correct sum = (36 x 50 + 48 -23) = 1825.
Correct mean = 1825 / 50 = 36.5.
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