Question

Question: 23
The second lowest number of five consecutive odd number series is four more than the 5/12th of the third Nghest number of a tive consecutive even number
series. If the average of five consecutive even number series is 60, then find the difference between the highest number of both the series?​

Answer 1

difference between then is 29

Answer 2

Answer:

Difference between the highest number of both the series = 29

Step-by-step explanation:

Let us take,

The five consecutive odd numbers be 2n-3, 2n-1, 2n+1, 2n-3, 2n+5, for any natural number 'n'

and the five consecutive even numbers be 2m-4, 2m -2, 2m, 2m+2, 2m+4, for any natural number 'm'

The second-lowest number in this odd number series = 2n-1

The third-highest number in the even number series  = 2m

Required to find,

Difference between the height number of both the series

Given,

The second-lowest number odd number series = 4 + $\frac{5}{12}$ X third-highest number in even number series.

That is,

2n - 1 = 4 + $\frac{5}{12}$ x 2m --------------(1)

Also given,

The average of the even numbers = 60

That is,

$\frac{2m-4+ 2m -2+ 2m+ 2m+2+ 2m+4}{5}$ = 60

$\frac{10m}{5} = 60$

2m = 60

Hence the even number series = 2m-4, 2m -2, 2m, 2m+2, 2m+4

= 60-4, 60-2, 60, 60+2, 60+4

= 56,58,60,62,64

The even number series = 56,58,60,62,64

From equation (1)  we get,

2n - 1 = 4 + $\frac{5}{12}$ x 60

2n -1 = 4 + 25 = 29

2n -1 = 29

2n = 30

Hence, the odd number series = 2n-3, 2n-1, 2n+1, 2n-3, 2n+5

= 30 -3, 30 - 1, 30 +1, 30+3, 30 +5

= 27, 29, 31, 33, 35

The odd number series  = 27, 29, 31, 33, 35

Difference between the highest number of both the series = 64- 35 = 29

Hence,

Difference between the highest number of both the series = 29