If a : b = 2 : 5, b : c = 5 : 8, c : d = 8 : 11, then a : d is:

a : b = 2 : 5

b : c = 5 : 8

c : d = 8 : 11

We need to find the combined ratio a : d.

To find the ratio a : d, we multiply the given ratios together. When two or more ratios are linked, the middle terms cancel out, and we are left with the ratio between the first and last terms.

given ratios:

​$$a : b = \frac{2}{5}, \quad b : c = \frac{5}{8}, \quad c : d = \frac{8}{11}$$​​

Now, by multiplying them

​$$\frac{a}{b} \times \frac{b}{c} \times \frac{c}{d} = \frac{2}{5} \times \frac{5}{8} \times \frac{8}{11} \\ \\ \\\Rarr \frac{a}{d} = \frac{2}{11}$$​​

Thus, the ratio a : d is 2 : 11.