Question

divide 40 into two parts such that 1/4th of one part is 3/8th of the other

Answer 1

let the two parts be a and b
so,
a/4 = 3b/8 ---> a/4 - 3b/8 = 0 ___ (i)
a + b = 40 ___ (ii)
(i) * 4:
a - 3b/2 = 0
(ii) - (i):
(a + b) - (a - 3b/2) = 40 - 0
b + 3b/2 = 40
5b/2 = 40
5b = 80
b = 16
from (ii):
a + 16 = 40
a = 24