The average of 35 consecutive natural numbers is N. Dropping the first 10 numbers and including the next 10 numbers, the average is changed to M. If the value of M² - N² = 600, then the average of 3M and 5N is:

115

By adding 10 next consecutive number , Average increses by 10 .

So , N+10 = M

ATQ ,

M2 - N2 = 600

(N+10)2 - N2 = 600

20N = 500

N = 25 &  M = 25 + 10 = 35

Sum  of 3M & 5N = 3×35 + 5 ×25 = 1=5 + 125 = 230

Average = \(\frac{230}{2}\)  = 115