Grade 9Algebra

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

Anmol Agarwal

10 Years agoGrade 9

4 Answers

Anoopam Mishra

Approved Tutor Answer10 Years ago

dinesh

10 Years ago

hey it is 27

Anmol Agarwal

10 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.