A contractor promised to hand over a job on the 30th day and put 20 equally skilled workers on it. At the end of the 18th day he found that only two-fifths of the job was done. How many extra workers of the same skill must he engage so that the job is still handed over on the 30th day?

In 18 days 20 workers put in 360 worker-days, and that covered two-fifths of the job, so the whole job is $360÷(2/5)=900$ worker-days. Three-fifths, or 540 worker-days, are left and only 12 days remain, so he needs 540 ÷ 12 = 45 workers on site — that is 45 − 20 = 25 extra. 45 is the total workforce required, not the addition asked for. 10 scales the gang by elapsed time against remaining time $(20\times 18/12=30)$ and ignores that three-fifths of the job is still untouched. 20 simply doubles the gang, which still leaves the job short.