THE BEANFEAST PUZZLE.

A number of men went out together on a bean-feast. There were four
Parties invited--namely, 25 cobblers, 20 tailors, 18 hatters, and 12
Glovers. They spent altogether $15.96. It was found that five cobblers
Spent as much as four tailors; that twelve tailors spent as much as nine
Hatters; and that six hatters spent as much as eight glovers. The puzzle
Is to find out how much each of the four parties spent.

25 cobblers, 20 tailors, 18 hatters, and 12 glovers.

five cobblers(C) spent as much as four tailors(T).
So, money spent by 5C = 4T
Multiplying both sides by 5,
25C = 20T
That means all the 25 cobblers spent equal to all the 20 tailors.
Considering that both parties has spent $x and $x

Now,
twelve tailors(T) spent as much as nine hatters(H),
So, money spent by 12T = 9H
Using unitary method,
when, 9 hatters spent equal to 12 tailors
Then, 1 hattes will spend equal to 12/9 tailors,
So, 18 hatters will spend equal to (12/9) * 18 tailors,
That makes, 18 hatters will spend equal to 24 tailors.

Now,
20 tailors has spent $x, then considering that all the tailors have spent equally,
4 tailors might spent $ x/5,
therefore 24 tailors has spent $ (x + x/5)
since 18 hatters will spend equal to 24 tailors, therefore 18 hatters has spent $ (x + x/5).

Now,
six hatters(H) spent as much as eight glovers(G),
So, money spent by 6H = 8G,
Using unitary method,
when, 8 glovers spent equal to 6 hatters
Then, 1 glover will spend equal to 6/8 tailors,
So, 12 glovers will spend equal to (6/8) * 12 tailors,
That makes, 12 glovers will spend equal to 9 tailors.
Which means that glovers has spent half of that of tailors.
Therefore, 12 glovers has spent $ (x + x/5)/2, because 24 tailors has spent $ (x + x/5).

now,
money spent by 25 cobblers + money spent by 20 tailors + money spent by 18 hatters + money spent by 12 glovers = $15.96
puttting the values of them,
x + x + (x + x/5) + (x + x/5)/2 = $15.96
On solving this we get, x = $4.2
Getting the value of (x + x/5) = $5.4
Getting the value of (x + x/5)/2 = $2.52

So,
money spent by 25 cobblers = money spent by 20 tailors = $4.2
money spent by 18 hatters = $5.4
money spent by 12 glovers = $2.52