Question

If a/b = 1/3, b/c = 2, c/d= 1/2, d/e= 3, e/f=1/4. Value of abc/def is ?

Answer 1

Find the value abc/def:

equate each of the letters to a single letter, say b.

cross multiply to find the value of the letters.

a/b = 1/3.............3a=b     therefore  a= b/3
b/c=  2 (that is 2/1) ......b= 2c   therefore c= b/2
c/d=1/2.......2c=d(from above 2c=b, hence d=b)...c=b/2
d/e=3....(d/e=3/1).......d=3e..therefore 3e=b,since b=d(from above) e=b/3
e/f=1/4...4e=f..(from above e=b/3, therefore f= 4 x b/3 = 4b/3

From the above calculations we have deduced the following:

a= b/3
b=b
c=b/2
d=b
e=b/3
f=4b/3

Hence abc/def :

abc=  b/3 x b x b/2
      =  (b x b x b) / (3 x 2)
      = b^3/6

def= b x b/3 x 4b/3
     =  (4 x b x b x b) /(3 x 3)
     =  4b^3/9
 

Therefore  abc/def  =   (b^3/6) / (4b^3/9)
                               =   b^3/6 x 9/4b^3......>b^3 cancels with b^3
                               =   1/6 x9/24
                               =    9/24
                               =   3/8
The answer =  3/8

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