Question

a group consisting of 25 teachers, 20 engineers, 18 doctors and 12 salesmen visited a fair and spent Rs 1330 altogether.It was found that 5 teachers spent as much as 4 engineers, 12 engineers spent as much as 9 doctors and 6 doctors spent as much as 8 salesmen.if every person in a professional gruop spent the same amount, find the amount spent by each engineer

Answer 1

Let amount spent by each teacher be t, the amount spent by each engineer be e, the amount spent by each doctor be d, and the amount spent by each salesman be s.
5t = 4e ...........(1)
Multiplying each side of (1) by 5 gives:
25t = 20e .......(2)

12e = 9d ........(3)
Multiplying each side of (3) by 2 and rearranging gives:
18d = 24e ......(4)

6d = 8s ...........(5)
Multiplying each side of (5) by 1.5 gives:
9d = 12s
But from (3) we have 12e = 9d
therefore
12s = 12e ........(6)
From the given details we can write:
25t + 20e + 18d + 12s = 1330 ...........(7)
Substituting values from (2), (4) and (6) into (7) we get:
20e + 20e + 24e + 12e = 1330 ..........(8)

Now you need to solve equation (8) to find the value of e, the amount spent by each engineer.