the ratio of the populations of town A and town B is 3:8, wheras the poulations of toen B and C is 5:2 , if the total population of the three towns is 85,342

$$\\A=\frac{3}{8}B\\\\
C=\frac{2}{5}B\\\\
(\frac{3}{8}+1+\frac{2}{5})B=85342\\\\
\frac{71}{40}B=85342\\\\
B=85432\times\frac{40}{71}=48080\\\\
A=48080\times\frac{3}{8}=18030\\\\
C=48080\times\frac{2}{5}=19232$$

Someone should post a more conventional answer to this one but this is how I would do it

First I want to make the Bs the same.  

3:8=15:40       and      5:2=40:16

so

check

$${\mathtt{18\,030}}{\mathtt{\,\small\textbf+\,}}{\mathtt{48\,080}}{\mathtt{\,\small\textbf+\,}}{\mathtt{19\,232}} = {\mathtt{85\,342}}$$     that is great.

YES, that is much neater, thanks Alan :))

A : B = 3 : 8,           B : C = 5 : 2     or    B : C = 8 : 3.2

Now we have this:     A : B : C = 3 : 8 : 3.2

Combine:    3+8+3.2 = 14.2

Divide:      85,342/14.2 = 6,010

Multiply  3, 8, and 3.2 by 6,010:

A       3*6,010 = 18,030

B       8*6,010 = 48,080

C       3.2*6,010 = 19,232

You did not explain how you got 3.2 anon.

@Melody:/   The ratio between A and B is 3:8, and between B and C is 5:2 ;

                   But I want the ratio between B and C to be 8:x

                   Let's find an x :

                   5/2 = 2.5         8/2.5 = 3.2     =>   x = 3.2

                   Now I have these 2 ratios:   A:B = 3:8,  and  B:C = 8:3.2

                   Out of these 2 ratios, I can create a 'triple' ratio:     A : B : C = 3 : 8 : 3.2

(Note that the ratios  5:2  and  8:3.2 are equal.)