Multiple choice

Find the values and state the correct relationship.\nIt takes ( (X-2) ) men to do a work in ( 2Y ) days and it takes ( (X+6) ) men to do the same work in ( Y ) days.\n\textbf{Quantity I:} ( X )\n\textbf{Quantity II:} ( Y )

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Work is constant, so (men × days) is constant. Therefore: (X-2)(2Y) = (X+6)(Y). Solving: 2XY - 4Y = XY + 6Y, so XY - 10Y = 0, giving Y(X - 10) = 0. Since Y cannot be 0, X = 10. Substituting back: (8)(2Y) = (16)(Y) gives 16Y = 16Y, which is satisfied for any positive Y. Thus X = 10 but Y cannot be uniquely determined, so the relationship cannot be established.

Keep practicing — related questions