If 30 men working 7 hours per day can do a work in 18 days, in how many days will 21 men working 8 hours a day do the same work?

 Let's assume that the amount of work to be done is 1 unit (it could be anything, as long as we use the same unit throughout the problem).

We can use the formula:

(work) = (rate) x (time)

Let's first find the rate of work for one man working for one hour.

For 30 men working 7 hours per day to complete 1 unit of work in 18 days:

(rate of work) = (30 men) x (7 hours/day) / (18 days) = 35/3 units per day

This means that one man working for one hour can complete 35/3 x 1/30 = 7/18 units of work.

Now, let's find how long it would take 21 men working 8 hours a day to complete the same 1 unit of work:

(work) = (rate) x (time)

1 unit = (21 men) x (8 hours/day) x (time) x (7/18 units per hour)

Simplifying this equation, we get:

time = 36 days

Therefore, 21 men working 8 hours a day can complete the same work in 36 days