Multiple choice

Passage

The following questions are accompanied by two statements A and B. You have to determine which statements(s) is/are sufficient/necessary to answer the questions.

Find the speed of boat in still water. (A) time taken to cover a distance of 18 km, first in upstream, then in downstream is 4 ½ hours. (B) If the speed of current gets doubled, then time taken to cover 18 km, first in downstream, then in upstream is 7 ⅕ hours.

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

  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 questions, 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
C Correct answer
Explanation

Let boat speed be b and current speed be c. Statement A gives 18/(b-c) + 18/(b+c) = 4.5. Statement B gives 18/(b+2c) + 18/(b-2c) = 7.2. Both equations are needed to solve for the two variables b and c.

AI explanation

Let the speed of the boat in still water be b and the speed of the current be c. From statement A, we get the equation 18/(b+c) + 18/(b-c) = 4.5, which has multiple possible values for b and c. From statement B, using the doubled current speed of 2c, we get 18/(b+2c) + 18/(b-2c) = 7.2, which provides a second equation; solving these two equations simultaneously is necessary to find the unique value of b. Thus, both statements taken together are necessary, but neither statement alone is sufficient.

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