Multiple choice

( (x-5) ) person can do a work in ( x ) days and ( (x+5) ) person can do 75 % of the same work in ( (x-11) ) days. Then in how many days can ( (x+10) ) person finish the work?

  1. 15 days

  2. 10 days

  3. 20 days

  4. 24 days

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

Using work = people × days, total work W = (x-5)(x). Also, 75% of W = (x+5)(x-11), so 0.75x(x-5) = (x+5)(x-11). Simplifying: 3x² - 15x = 4x² - 11x + 5x - 55, which gives x² - x - 55 = 0. Solving: x = 10 (valid) or x = -9 (invalid). Total work W = 10(5) = 50 person-days. For (x+10) = 20 people: days = 50/20 = 2.5 days.

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