Multiple choice

Directions: The following question is accompanied by statements A and B. You have to determine which statement(s) is/are sufficient/necessary to answer the question. Roopesh can complete a piece of work in x days. Heena can complete the same work in (x + 30) days and Ramesh can complete the same job in (x + 60) days. Find the value of x. (A) Roopesh and Heena together can complete the same job in 20 days. (B) Roopesh and Ramesh together can complete the same job in 45/2 days.

  1. Statement A alone is sufficient to answer the question, but statement B alone is not sufficient to answer the question.

  2. Statement B alone is sufficient to answer the question, but statement A alone is not sufficient to answer the question.

  3. Both the statements taken together are necessary to answer the question, but neither of the statements alone is sufficient to answer the question.

  4. Either statement A or statement B by itself is sufficient to answer the question.

  5. Statements A and B taken together are not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the work be 1 unit. Rates are 1/x, 1/(x+30), 1/(x+60). Statement A gives 1/x + 1/(x+30) = 1/20, which is a quadratic in x. Statement B gives 1/x + 1/(x+60) = 2/45, also a quadratic in x. Both equations are sufficient to solve for x.

AI explanation

Using the statement A equation, 1 divided by x plus 1 divided by the quantity x plus 30 equals 1 by 20, which simplifies to x squared minus 10x minus 600 equals 0. Solving this quadratic equation yields the value of x as 30. Using statement B, the equation 1 divided by x plus 1 divided by the quantity x plus 60 equals 2 by 45 simplifies to x squared minus 15x minus 900 equals 0, which also gives a valid positive value for x. Since both statements independently form solvable equations, either one alone is sufficient.

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