Multiple choice

The work done by (x - 3) men in (2x + 1) days and the work done by (2x + 1) men in (x+4) days are in the ratio of 3 :10. Find the value of x.

  1. 3

  2. 5

  3. 6

  4. 2
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C Correct answer
Explanation

Work done is proportional to (men * days). Thus, ((x-3)(2x+1)) / ((2x+1)(x+4)) = 3/10. Canceling (2x+1) gives (x-3)/(x+4) = 3/10. Solving 10x-30 = 3x+12 leads to 7x=42, so x=6.

AI explanation

The amount of work done is directly proportional to the number of men multiplied by the number of days. The given ratio equation is ((x - 3)(2x + 1)) / ((2x + 1)(x + 4)) = 3/10. Canceling out the common (2x + 1) term gives (x - 3) / (x + 4) = 3/10. Cross-multiplying and solving the resulting equation 10x - 30 = 3x + 12 gives 7x = 42, so x is 6.

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