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 ?

If each bank employee spent x rupees, then each dentist spent 4x/3 and each doctor spent x and each writer spent 4x/5. As there were 25 writers, 20 doctors, 18 dentists and 12 bank employees, the total spent, in terms of x, is 20x + 20x + 24x + 12x (the terms representing writers, doctors, dentists and bank employees respectively), which is 76x. Setting 76x=1330, we get x=17.50.

In total the writers spent 350 rupees, the doctors also 350 rupees, the dentists 420 rupees and the bank employees 210 rupees.

The dentists at least must have spent different amounts from each other, at least by 1 paise within each group of 3, as dividing 420 by 18 gives a non-terminating decimal. (Equivalently, 4*17/3 is non-terminating.)

Posted by Charlie on 2003-03-23 06:07:48