Multiple choice

Sonia, Arjun, and Priya, working together, would have taken at least 10 days to complete a project. Sonia and Priya, working together, would have taken less than 25 days to complete the same project. In reality, all three worked together for 8 days, followed by Arjun, who worked alone for 4 more days to finish the project. If Arjun had worked alone on the project, then the number of days he would have taken to complete it cannot be

  1. 17

  2. 18

  3. 19

  4. 20
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let S, A, P be the work rates. (S+A+P) >= 1/10. (S+P) < 1/25. 8(S+A+P) + 4A = 1. If Arjun takes T days, A = 1/T. 8(S+P+1/T) + 4/T = 1 => 8(S+P) + 12/T = 1. Since S+P < 1/25, 8(S+P) < 8/25 = 0.32. So 1 - 12/T < 0.32 => 12/T > 0.68 => T < 17.64. Also (S+A+P) >= 1/10 => 1/T + (S+P) >= 1/10. Since S+P < 1/25, 1/T > 1/10 - 1/25 = 3/50 = 0.06 => T < 16.66. The value 17 is not possible.

AI explanation

Let the one day work of Sonia, Arjun, and Priya be S, A, and P respectively, and the total work be 1 unit. The first condition means S plus A plus P is less than or equal to 1/10, while the second means S plus P is greater than 1/25. The actual completion gives the equation 8 times (S plus A plus P) plus 4A equals 1, which simplifies to 2 times (S plus A plus P) plus A equals 1/4. Subtracting the first condition from this equation yields A is greater than or equal to 1/20, so Arjun takes at most 20 days. Subtracting the equation from 1 and using the second condition yields 1/4 minus A is greater than 1/25, meaning A is less than 1/20, so Arjun takes strictly more than 19 days. Combining these shows Arjun takes exactly 20 days, making 17 days an impossible value.

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