Anjali alone can do a piece of work in (x) days and Shalu alone can do the same work in (x+5) days. If Anjali and Shalu together can complete the same work in (11\frac{1}{9}) days, then find the number of days required by Anjali to complete the work alone?

Work rate formula: If Anjali takes x days and Shalu takes (x+5) days alone, their combined rate is 1/x + 1/(x+5) = 1/(11⅑) = 9/100. Solving: (2x+5)/(x²+5x) = 9/100, which gives 9x² + 45x - 200x - 500 = 0, or 9x² - 155x - 500 = 0. Using quadratic formula: x = [155 ± √(24025 + 18000)]/18 = [155 ± √42025]/18 = [155 ± 205]/18. Since x must be positive, x = (155 + 205)/18 = 360/18 = 20. Therefore Anjali alone takes 20 days.