Multiple choice

Directions: The question given below is followed by three statements (A), (B) and (C). You have to determine which statement(s) is/are sufficient/necessary to answer the question. In how much time can 15 boys and 21 girls do the same work? A. 6 boys and 9 girls can do a piece of work in 12 days. B. One girl can complete the work in 468 days. C. 23 boys and 41 girls can do the same work in 3 days.

  1. Only statement A

  2. Only statement B

  3. Any two of them

  4. Either A or B

  5. All three statements
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let B be the work rate of a boy and G be the work rate of a girl. A: 6B + 9G = 1/12. B: G = 1/468. C: 23B + 41G = 1/3. With B and G, we have two variables. Any two equations are sufficient to solve for B and G, which then allows calculating the time for 15B + 21G.

AI explanation

The question asks to find the time taken by 15 boys and 21 girls, which requires determining the individual efficiencies of both boys and girls. Any two statements from A, B, and C will form a pair of independent linear equations in two variables. Since two distinct linear equations are always sufficient to find the unique values of the two variables (the efficiencies of a boy and a girl), any pair will provide the necessary values to calculate the required time. Therefore, any two of the given statements are sufficient to answer the question.

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