The average of 35 consecutive natural number is N. Dropping the first 10 number and including the next 10 numbers affect the average changed to M. If M² - N² = 600, then find the value of M and N.

35, 25

Method 1:

go with option (B):

M = 35, N = 25,

ATQ, M² - N² = 35² - 25² = 1225 - 625 = 600 (only this option justify the question)

Method 2: 

The average of 1 to n consecutive natural number = \(\frac{n + 1}{2}\) = N

The average of (1+ 10) to (n + 10) consecutive natural number = \(\frac{n + 10 + 1 + 10}{2}\) = \(\frac{n + 1 + 20}{2}\) = \(\frac{n + 1}{2}\) + 10 = N + 10 = M

So,

M - N = 10 .... (i)

ATQ, M² - N² = 600

(M - N) (M + N) = 600

(10) (M + N) = 600

M + N = 60 .... (ii)

From equation (i) and (ii)

M - N = 10

M + N = 60

Therefore, M = 35, N = 25