If $a:b=\frac{2}{3}:\frac{1}{4}$ and $b:c=\frac{3}{4}:\frac{4}{5}$, then find $a:b:c$.

40:15:16

$a:b=\frac{2}{3}:\frac{1}{4}$

a/b = 8/3

a = 8b/3

$b:c=\frac{3}{4}:\frac{4}{5}$

b/c = 15/16

b = 15c/16

a/c = 8/3 * 15/16

a/c = 5/2

c = 2a/5 = (2*8b)/(5*3)

a:b:c = 8b/3 : b : 16b/15

Multiplying and dividing all the ratios by 15

a:b:c = 40/15 : 15/15 : 16/15 = 40:15:16 

The correct answer is Option (4) → 40:15:16