Multiple choice

The question below consists of a question and three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answer. Three workers A, B and C complete a work together in 4 days. The time taken by A and B together to complete the 25% of the whole work is equal to the time taken by D and C together to complete the 150% more than the 1/10th of the whole work. In how many days, D will complete the whole work alone? Statement I: Efficiencies of A and D are in the ratio 5: 3 respectively. Statement II: Efficiencies of B and C are in the ratio 2: 3 respectively. Statement III: Efficiency of D and C are in the ratio 1: 2 respectively.

  1. Either statement I or II or III alone is sufficient.

  2. Either statement III alone is sufficient or statement I and II together are sufficient.

  3. Either statement II alone is sufficient or statement I and III together are sufficient.

  4. Either statement I and II or statement II and III together are sufficient.

  5. Any of the two statements together are sufficient.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement III alone is sufficient because it directly gives D:C efficiency ratio as 1:2. Since A+B+C complete work in 4 days, and we have the relationship between (A+B) doing 25% work and (D+C) doing 150% more than 1/10th (i.e., 25% of work), we can equate: (A+B) time = (D+C) time. This with the D:C ratio gives individual efficiencies, hence D's time alone. Statements I and II together also work: I gives A:D = 5:3, II gives B:C = 2:3, combined with the work relationship allows solving.

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