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Repdigit numbers 11...1 and 99...9 written as (10^n - 1)/9

This type of question, asked 2 times: CDS 2 2017, CDS 1 2020. All 2 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2017

    4
    If x=111…1x = 111 \ldots 1 (20 digits), y=333…3y = 333 \ldots 3 (10 digits) and z=222…2z = 222 \ldots 2 (10 digits), then what is x−y2z\frac{x - y^2}{z} equal to ?

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  2. Question 2

    CDS 1 2020

    6
    If the sum of the digits of a number 10n−110^{n} - 1, where nn is a natural number, is equal to 3798, then what is the value of nn ?

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