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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

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

Grade:9

4 Answers

Anoopam Mishra
126 Points
8 years ago
17
dinesh
22 Points
8 years ago
hey it is 27
 
Anmol Agarwal
10 Points
8 years ago
Answer is 18
Answer is 18

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 digit99999⋯9remaining n/9 digits

Now it is given that S(N)=2013

We know that 2013=6+9∗223

            ⟹N=(6)999999⋯9223 times

⟹5N=(34)9999⋯9222 times(5)

⟹5N+2013=(34)9999⋯9222 times(5)+2013

⟹5N+1023=(35)0000⋯0219 times(2008)

⟹S(5N+1023)=3+5+2+0+0+8=18

Therefore required answer is 18.
SHANMUKESHWAR
461 Points
8 years ago
5+2+0+1+3+2+0+1+3=17
 

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