[ROLCAM]

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.

[shatriya]

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