It was expected that 10 men together would complete a piece of work in 40 days. But after a few days, they increased their efficiency by 25% and completed the work six days earlier. How many days after the start of the work did they increase their efficiency?

Let x be the days worked at normal efficiency. Total work = 10 * 40 = 400 man-days. After x days, 10x work is done. Remaining work = 400 - 10x. Efficiency increases by 25%, so new rate is 12.5 men. They finish in (40 - x - 6) = 34 - x days. Equation: 10x + 12.5(34 - x) = 400. 10x + 425 - 12.5x = 400. 2.5x = 25, so x = 10.