Multiple choice

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

  1. 6

  2. 7

  3. 8

  4. 9
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Work = men * days. x = (3n - 1)(2n + 1) = 6n^2 + n - 1. y = (3n + 1)(4n - 3) = 12n^2 - 5n - 3. x/y = 6/11. 11(6n^2 + n - 1) = 6(12n^2 - 5n - 3). 66n^2 + 11n - 11 = 72n^2 - 30n - 18. 6n^2 - 41n - 7 = 0. Solving for n: (6n + 1)(n - 7) = 0. n = 7.

AI explanation

By the man-days formula, the ratio of work x to y is the ratio of their total efforts, giving ((3n - 1)(2n + 1)) / ((3n + 1)(4n - 3)) = 6 / 11. Cross-multiplying this equation yields 11 times (6n^2 + n - 1) equals 6 times (12n^2 - 5n - 3), which simplifies to 6n^2 - 41n - 7 = 0. Solving this quadratic equation provides the values n = 7 or n = -1/6, making the valid integer value 7.

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