Multiple choice

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

  1. 8

  2. 10

  3. 12

  4. 15
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Work done is proportional to (workers * days). So, (x+2)(x-3) / (x+4)(x-2) = 3/4. Expanding gives 4(x^2 - x - 6) = 3(x^2 + 2x - 8). 4x^2 - 4x - 24 = 3x^2 + 6x - 24. x^2 - 10x = 0. Since x must be positive, x = 10.

AI explanation

The work done is proportional to the product of the number of workers and the number of days, which gives the equation ((x + 2)(x - 3)) divided by ((x + 4)(x - 2)) equals 3 divided by 4. Cross-multiplying yields 4 times (x squared minus x minus 6) equals 3 times (x squared plus 2x minus 8), simplifying to x squared minus 10x equals 0. Factoring out x gives x(x - 10) = 0, and since the number of days must be positive, x is 10.

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