Question

If digits of 5 digit no. In base N is increased by 1. The decimal value of no. Increases bY 16105 . What is the sum of digits N?

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

Step-by-step explanation:

Given

digits of 5 digit no. In base N is increased by 1. The decimal value of no. Increases bY 16105.

Explanation:

Let the five digits of the number having base N be denoted by a, b, c, d, and e.

Let the number in the decimal system be denoted by 'S'.

Then the number in the decimal system can be given as,

number−>(abcde) N

−>aN 4 +bN 3 +cN 2 +dN+eN 0 =(S) 10

−>aN 4 +bN 3 +cN 2 +dN+e=S

When each digit is increased by one we get,

−>(a+1)N 4 +(b+1)N 3 +(c+1)N 2 +(d+1)N+(e+1)N 0 =S+16105

−>aN 4 +bN 3 +cN2+dN+e+N 4 +N 3 +N 2 +N+1=S+16105

−>N 4 +N 3 +N 2+N+1=16105

−>N 4 +N 3 +N 2 +N=16104

−>N(N3+N2+N+1)=11(1331+121+11+1)

−>N=11

Hence we have N=11 and the sum of digits of N is 2