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# S(M) denotes the sum of the digits of a positive integer M written in base 10.Let N be the smallest positive integer such that S(N)=2013,then find S(5N+2013)=?Example:S(201)=2+0+1=3

Anoopam Mishra
126 Points
6 years ago
17
dinesh
22 Points
6 years ago
hey it is 27

Anmol Agarwal
10 Points
6 years ago

Explanation :

Given that

S(M) denotes the sum of the digits of a positive integer M written in base of 10.

Let N be the smallest positive integer such that S(N)=n.

Now observe that 9 as an individual contributes more to n.

So, the number N will be as follows

N=(nmod9)first digit999999remaining n/9 digits

Now it is given that S(N)=2013

We know that 2013=6+9223

N=(6)9999999223 times

5N=(34)99999222 times(5)

5N+2013=(34)99999222 times(5)+2013

5N+1023=(35)00000219 times(2008)

S(5N+1023)=3+5+2+0+0+8=18