Multiple choice

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

  1. 8

  2. 9

  3. 10

  4. 12
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A Correct answer
Explanation

Work = Men * Days. y = (x-1)(x+1) = x^2 - 1. z = (x+2)(x-1) = x^2 + x - 2. Ratio y/z = (x-1)(x+1) / ((x+2)(x-1)) = (x+1)/(x+2) = 9/10. 10x + 10 = 9x + 18. x = 8.

AI explanation

Work is proportional to the product of the number of men and the number of days, so y equals (x - 1)(x + 1) and z equals (x + 2)(x - 1). Given the ratio y : z = 9 : 10, we can write the proportion as [(x - 1)(x + 1)] / [(x + 2)(x - 1)] = 9 / 10. Canceling (x - 1) from both sides leaves (x + 1) / (x + 2) = 9 / 10. Cross-multiplying yields 10x + 10 = 9x + 18, which simplifies to x = 8.

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