If A : B = 7 : 5, B : C = 2 : 3, and C : D = 4 : 5, find the ratio A : D.

Correct option is C

Given:

A : B = 7 : 5
B : C = 2 : 3
C : D = 4 : 5

Solution:
​$$\frac{A}{B} = \frac{7}{5}, \frac{B}{C} = \frac{2}{3}, \frac{C}{D} = \frac{4}{5}$$​, then

$$\frac{A}{D} = \frac{A}{B} \times \frac{B}{C} \times \frac{C}{D} \\ \ \\\frac{A}{D} = \frac{7}{5} \times \frac{2}{3} \times \frac{4}{5}\\ \ \\= \frac{7 \times 2\times 4}{5\times 3\times 5}\\ \ \\= \frac{56}{75}$$​

Thus,
A : D = 56 : 75.