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 ?
Let the respective amounts spent by all the writers, all the doctors, all the dentists and all the bank employees be a, b, c and d.
By the problem, the ratio between the amount spent by each writer, and each dentist is 4:5, and so a/b = 100/100 = 1
The ratio between the amount spent by each doctor, and that of each dentist is 4:5, and so b/c = 60/72 = 5/6
The ratio between the amount spent by each dentist, and each bank employee is 3:, and so c/d = 72/36 = 2
Consequently, a:b:c:d = 5:5:6:3, and thus:
(a,b,c,d) = (5x,5x,6x,3x) for some x.
By the given conditions, we must have:
5x+5x+6x+3x = 1330
Or, 19x = 1330, giving:
x = 70, so that:
(a,b,c,d) = (350, 350, 420, 210)
Consequently, the respective amounts spent by all the writers, all the doctors, all the dentists and all the bank emplorees are Rs. 350, Rs. 350, Rs.420 and Rs. 210.
Edited on November 29, 2007, 12:19 pm
puzzle solution
