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I edited the post, replacing "cut the field" by "plow the field" and "labourers" by "laborers" everywhere.
8 laborers plow a field in 6 days.
(a) how many men will plow the field in 3 days?
(b) how long will it take 12 men plow the field?
(c) how long will it take 10 men to plow the field?
(d) how long will it take 20 laborers plow the field?
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Solution
There are two ( or three :) ) standard ways to solve problems like these and to explain the solution.
First way
(a) The entire work requires 8*6 = 48 labor-days.
To find how many laborers "x" are needed to complete the job in 3 days, write an equation
48 = 3x, (1)
which immediately gives the solution and the answer
x = 48/3 = 16 days.
Second way
(a) The rate of work of each laborer is of the entire job per day in the first case.
In the second case, the rate of work of each laborer is of the job per day
Assuming that the rate of work is the same in both cases, you get an equation
= .
From the equation, you get
8*6 = 3x ( ! same equation as (1) (!) ), so
x = = 16.
You get the same answer.
Third way
When you solve such problems several times, you will find it OBVIOUS that two times shorter time period requires two times larger team.
Armed with this knowledge, you can easily solve the rest of problems by any of these three ways ON YOUR OWN.