Average
- The average of x numbers is y2 and the average of y numbers is x2. So the average of all the numbers taken together is
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Total sum of x numbers = xy2
Total sum of y numbers = yx2∴ Required average = xy2 + yx2 x + y ∴ Required average = xy(y + x) = xy x + y
Second method to find the required average ,
Here, n1 = x, a1 = y2
n2 = y, a2 = x2∴ Average = n1a1 + n2a2 n1 + n2
Correct Option: B
Total sum of x numbers = xy2
Total sum of y numbers = yx2∴ Required average = xy2 + yx2 x + y ∴ Required average = xy(y + x) = xy x + y
Second method to find the required average ,
Here, n1 = x, a1 = y2
n2 = y, a2 = x2∴ Average = n1a1 + n2a2 n1 + n2 Average = xy2 + yx2 x + y Average = xy 
x + y 
= xy x + y
- The average of n numbers x1, x2, .... xn is x . Then the value of ⅀(xi - x) , ( i = 1 .......... n ) is equal to
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As we know that ,
x = x1 + x2 + . . . .xn n 
= (x1 - x) + (x2 -x) +....... + (xn - x)
= (x1 + x2 + . . . . . + xn) - n . x
Correct Option: B
As we know that ,
x = x1 + x2 + . . . .xn n = (x1 - x) + (x2 -x) +....... + (xn - x)
= (x1 + x2 + . . . . . + xn) - n . x= n. x1 + x2 + . . . .xn - n.x n
= nx - nx = 0
- A man bought 13 articles at ₹ 70 each, 15 at ₹ 60 each and 12 at ₹ 65 each. The average price per article is
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We can find the required average with the help of given formula ,
Here, n1 = 13 , a1 = 70
n2 = 15 , a2 = 60 , n2 = 12 , a2 = 65∴ Average = n1a1 + n2a2 + n3a3 n1 + n2 + n3 Required average price = 13 × 70 + 15 × 60 + 12 × 65 13 + 15 + 12
Correct Option: B
We can find the required average with the help of given formula ,
Here, n1 = 13 , a1 = 70
n2 = 15 , a2 = 60 , n2 = 12 , a2 = 65∴ Average = n1a1 + n2a2 + n3a3 n1 + n2 + n3 Required average price = 13 × 70 + 15 × 60 + 12 × 65 13 + 15 + 12 Required average price = 910 + 900 + 780 40 Required average price = 2590 = ₹ 64.75 40
- The average of 20 numbers is 15 and the average of first five is 12. The average of the rest is
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If the average of remaining numbers be n, then
20 × 15 = 5 × 12 + 15n
⇒ 300 = 60 + 15n
⇒ 15n = 300 – 60 = 240⇒ n = 240 = 16 15
Second method to find the required average ,
Here, m = 20, x = 15 n = 5, y = 12Average of remaining
Numbers =mx - ny mn Average of remaining
Numbers =20 × 15 - 5 × 12 20 - 5
Correct Option: A
If the average of remaining numbers be n, then
20 × 15 = 5 × 12 + 15n
⇒ 300 = 60 + 15n
⇒ 15n = 300 – 60 = 240⇒ n = 240 = 16 15
Second method to find the required average ,
Here, m = 20, x = 15 n = 5, y = 12Average of remaining
Numbers =mx - ny mn Average of remaining
Numbers =20 × 15 - 5 × 12 20 - 5 Average of remaining
Numbers =300 - 60 15 Average of remaining
Numbers =240 = 16 15
- 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 (in kg) of B is
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Weight of B = (A + B)’s weight + (B + C)’s weight – (A + B + C)’s weight
Weight of B = 40 × 2 + 43 × 2 – 45 × 3
Weight of B = 80 + 86 – 135Correct Option: C
Weight of B = (A + B)’s weight + (B + C)’s weight – (A + B + C)’s weight
Weight of B = 40 × 2 + 43 × 2 – 45 × 3
Weight of B = 80 + 86 – 135
Weight of B = 166 – 135 = 31 kg.
