A number of us went out together to a charity fete one day. Our party consisted of four different professional groups, namely – 25 writers, 20 doctors, 18 dentists and 12 bank employees. We spent altogether Rs. 1330.

Later it was found that 5 writers spent as much as 4 doctors, that 12 doctors spent as much as 9 dentists and that 6 dentists spent as much as 8 bank employees.

[Or, in other words: "A Writer spent (4/5) times the amount spent by a Doctor, a Doctor spent (3/4) times the amount spent by a Dentist and a Dentist spent (4/3) times the amount spent by a Bank Employee].

How much did each of the four professional groups spend ?

It is not altogether clear in the statement of the problem, but I think we are supposed to assume that the members of each group spent the same amount. If that is the case, we can state:

let x = amount spent by bank employee
4x/3 = amount spent by dentist
(3/4)(4x/3) = x = amount spent by doctor
4x/5 = amount spent by writer

Therefore, the total amount spent is:
25(4x/5) + 20x + 18(4x/3) + 12x = 1330
20x + 20x + 24x + 12x = 1330
76x = 1330
x = 17.5

The writers and doctors spent (each group) 20x = 350 Rs.
The dentists spent 24x = 420 Rs.
The bank employees spent 12x = 210 Rs.

And just to check: 350+350+420+210 is indeed 1330.

Posted by DJ on 2003-03-23 10:33:16