The average of squares of five consecutive even natural numbers is 792. The ratio of smallest number

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29 Apr 2022 Number System

The average of squares of five consecutive even natural numbers is 792. The ratio of smallest number to largest number is

OPtion

1) 4 : 5
2) 3 : 4
3) 5 : 6
4) 2 : 3
5) 7 : 8
6) 6 : 7
7) 13 : 15
8) 15 : 16
9) 13 : 17
10) None of these

Solution

Let the five consecutive even numbers be x, (x+2), (x+4), (x+6), (x+8)
Average of squares of these numbers = [x² + (x+2)² + (x+4)² + (x+6)² + (x+8)²] / 5 = 792
x² + x² + 4x + 4 + x² + 8x + 16 + x² + 12x + 36 + x² + 16x + 64 = 3960
5x² + 40x - 3840 = 0
x² + 8x - 768 = 0
(x+32) (x-24) = 0
x = -32, 24
Considering +ve value of a natural number, x=24
.'. The numbers are 24, 26, 28, 30, 32
Required ratio = 24/32 = 3/4

Correct Option: 2 Best Solution (1)

Mayank Kandoi   2 years AGO

Let the numbers are......(n-4), (n-2), n, (n+2), (n+4)

(n-4)² + (n-2)² + n² + (n+2)² + (n+4)² = 792 * 5
2 (n²+16) + 2 (n²+4) + n² = 3960
5n² + 40 = 3960
5n² = 3920
n = 28

Smallest number = n-4 = 24
Largest number = n+4 = 32
Ratio = 24:32 = 3:4

Option 2

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