Multiple choice

Vijay alone completes a work in 15 days. In how many days Alok alone can complete that work? I. The ratio of their efficiencies of Vijay and Alok is 3:1 respectively. II. Completing 33.33% of total work Alok alone takes 10 days more than Vijay alone. III. Both working together completes the work in 11.25 days

  1. I and II together

  2. II and III together

  3. All three together

  4. All together are not sufficient

  5. None of these
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Given Vijay takes 15 days alone, so his efficiency is 1/15 per day. Statement I gives Vijay:Alok efficiency ratio as 3:1, so Alok's efficiency is 1/45, meaning he takes 45 days. Statement II: 33.33% = 1/3 of work by Alok takes 10 days more than Vijay for full work. Vijay takes 15 days, so Alok takes 15 + 10 = 25 days for full work. This contradicts Statement I. Statement III: Together they take 11.25 days, so combined efficiency = 1/11.25. With Vijay at 1/15, Alok would be 1/45, taking 45 days - again contradicting Statement II. The statements are inconsistent, but any one with the given data is sufficient, making 'None of these' correct.

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