Amit can do 3 4th of work in 5 6 days in comparison to Bhanu. If both complete the work in 10 days doing together then in how many days Bhanu alone can finish the work?

If Amit does 3/4 of work in 5/6 of Bhanu's time, Amit's rate : Bhanu's rate = (3/4)/(5/6) = 9:10. Together in 10 days: (9+10)/10k = 1/10, so k = 1. Bhanu alone: 10/1 = 10 days for full work. But wait - let me recalculate. Amit's efficiency = (3/4 work)/(5/6 time) = 9/10 of Bhanu. So if Bhanu takes x days, Amit takes x/(9/10) = 10x/9 days. Together: 1/x + 9/(10x) = 1/10. 19/(10x) = 1/10, x = 19. Bhanu takes 19 days.