If a/b = 2/3, b/c = 1, c/d = 1/2, d/e = 3 and e/f = 1/2 then what is the value of abc/def?

Question

If
a/b = 21/34;
b/c = 121/120;
c/d = 17/77;
e/f = 11/15
and
d/e = 14/17
then what is the value of
(abc/def)*2?

Answer 1

a=2/3b=2/3c=d/3=e=f/2
abc=(f/2)x(3/4f)x(3/4f) = 9/32f3
def=(3/2f)x(f/2)x(f)=3/4f3
abc/def=(9/32)/(3/4)=3/8

Answer 2

3/8
(a/b)*(b/c)*(c/d)=(2/3)*(1)*(1/2)=a/d=1/3
(b/c)*(c/d)*(d/e)=(1)*(1/2)*(3)=b/e=3/2
(c/d)*(d/e)*(e/f)=(1/2)*(3)*(1/2)=c/f=3/4
multiply the three=a.b.c/(d.e.f)=3/8

Answer 3

another way of solving the same is let a=2, then b=3, c=3, d=6,e=2 and f=4. now a.b.c/(d.e.f)=2*3*3/(6*2*4)=3/8