A gang of masons can build a boundary wall in 24 days working at a steady rate. They keep that rate for the first 9 days, but from the 10th day onward the monsoon cuts their daily output to two-thirds of what it was. The wall is finished in how many days altogether?

In 9 days they finish 9/24 = 3/8 of the wall, so 5/8 is left — the equivalent of 15 more days at the old rate. At two-thirds of that rate the same stretch takes $15\times 3/2=22.5$ days, giving 9 + 22.5 = 31.5 days in all. (Cutting output to two-thirds multiplies the time by 3/2, not by 4/3: adding only a third more time gives 9 + 20 = 29 days. Stretching the WHOLE 24 days by 3/2 gives 36 and ignores the nine good days; 33 restarts the full 24-day clock on day 9.)