if 14 men can cultivate 42 acres of land in 18 weeks how many week will 21 men working at the same rate take to cultivate 56 acres of land

Answer 1

42 acres requires 14*18 man-weeks of work
so, 56 acres requires 56/42 * 14*18 man-weeks of work
Now divide that by 21 men and you get 16 weeks

Or, note that you have
3/2 the men, so 2/3 the time
4/3 times the area, so 4/3 times the time
18 * 2/3 * 4/3 = 16

or, as a word problem,
The time it takes to clear a field varies directly with the area, and inversely with the number of men. So,

t = ka/m

That is, tm/a = k, a constant
So, you want t such that
t*21/56 = 18*14/42
t = 16

Answer 2

or
14 men can cultivate 42 acres of land in 18 weeks
1 man can cultivate 42/14 or 3 acres of land in 18 weeks
1 man can cultivate 1 acre of land in 6 weeks
21 men can cultivate 1 acre of land in 6/21 or 2/7 weeks
21 men can cultivate 56 acres of land in 2/7(56) or 16 weeks