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.
Answer & explanation
Correct answer: option 2
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