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Work by (x+a) men in (x+b) days vs (x+c) men in (x+d) days in a given ratio: find x

The same question, asked 4 times: CDS 1 2019*, CDS 1 2021*, CDS 2 2021*, CDS 1 2024. Every wording below, oldest first.

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  1. Question 1

    CDS 1 2019

    94
    If the ratio of the work done by (x+2)(x + 2) workers in (x−3)(x - 3) days to the work done by (x+4)(x + 4) workers in (x−2)(x - 2) days is 3:43 : 4, then what is the value of xx ?

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  2. Question 2

    CDS 1 2021

    40
    Let the work done by (x−1)(x - 1) men in (x+1)(x + 1) days be yy. Let the work done by (x+2)(x + 2) men in (x−1)(x - 1) days be zz. If y:z=9:10y : z = 9 : 10, then what is the value of xx?

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  3. Question 3

    CDS 2 2021

    28
    Let work done by (3n−1)(3n-1) men in (2n+1)(2n+1) days be xx and work done by (3n+1)(3n+1) men in (4n−3)(4n-3) days be yy. If x:y=6:11x:y=6:11, then what is the value of nn ?

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  4. Question 4

    CDS 1 2024

    45
    If the work done by x men in (x+1)(x + 1) days is equal to the work done by (x+5)(x + 5) men in (x−2)(x - 2) days, then what is the value of x ?

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