The average of 4 consecutive even numbers is 27. What is the greatest number

Let's eight sequentially number are x, x + 1, x + 2, x + 3, x + 4, x + 5, x + 6 and x + 7.
According to the question [(x + 3) + (x + 4)]/2 = 6
? (2x + 7)/2 = 6 ? 2x + 7 = 12
? 2x = 5 ? x = 5/2

? Sum of all eight numbers = x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 + x + 6 + x + 7
= 8x + 28
= 20 + 28
= 48

Average of 5 boys = 16 yr
sum of age of 5 boys = 16 x 5 = 80 yr
? Average age of 4 boys = 16 - yr 3 month
= 16 yr + 3/12 yr = 16 yr + 1/4 yr
Sum of ages of 4 boys = 4 x (16 +1/4) yr
= 64 +1 = 65 yr
? Age of 5th boy = (80 - 65) yr = 15 yr

Average of 8 numbers = 14
Sum of 8 numbers = 14 x 8 = 112
Similarly, average of 6 numbers = 16
Sum of 6 number = 16 x 6 = 96
? Sum of remaining two number
= Sum of 8 number - sum of 6 numbers
= 112- 96 = 16
Average = (sum of two number)/2 = 16/2 = 8

As per the formula,
Average of the cubes os 1st 'n' natural numbers= n(n+1)²/4
where, n= 5.

? Required average = 5(5+1)²/4
= (5 x 36)/4 = 5 x 9= 45

Even numbers between 11 to 63
= 12,14,16,18,20,..........,62.
Clearly, this is a series of consecutive even number

According to the formula
Average of consecutive even numbers = (First number + Last number)/2
= (12 + 62)/2
= 74/2
= 37

Total cost of 30 TV sets = ? 300000
Total cost of 15 TV sets = 9000 x 15 = 135000
Total cost of remaining 15 TV sets = 300000 - 135000 = 165000

? Average cost of remaining TV sets = 165000/15 = ? 11000

Total age of 30 girls = 30 x 13 = 390 yr
Total age of 18 girls = 18 x 15 = 270 yr.
? Age of remaining 12 girls = 390 - 270 = 120 yr
? Required average = 120/12 = 10 yr

Let the numbers A, B, C, and D are N , N+1, N + 2 and N + 3, respectively.
According to the question,
[N + (N+1) + (N+2) + (N+3)] / 4 = 49.5
? 4N + 6 = 4 x 49.5
? 4N = 198 - 6 ? N = 192/4
? N = 48

The required product = B x D
= (N + 1) x (N + 3)
= (48 +1) (48 +3 )
= 49 x 51
= 2499

Overall height = (n₁a₁ + n₂a₂) / (n₁ + n₂)
n₁= 20,
a₁ = 5 ft 11 inches = 5 x 12 + 11 = 71 inches
n₂= 18,
a₂ = 6 ft 2 inches = 6 x 12 + 2 = 74 inches

? Overall height = [(20) (71) + (18) (74)] / (20+18)
= (1420 + 1332) / 38 = 72.42 inches

According to the fundamental to the fundamental formula
Average(A)= Sum (S) / Number(N)

From the question 60 = S / 13
? S = 60 x 13 = 780

Sum of first seven result = 59 x 7 = 413
Sum of last seven result = 61 x 7 = 427

? 7th result = (Sum of first seven result) + (Sum of last seven results) - (Sum of all the results)
= (413 + 427 - 780 )
= (840 - 780)
= 60

NoteSum of first seven when added to the sum of last seven result, then repetition of 7th result takes place.