Find the compounded ratio of $ 2:3 $ and $ 5:7 $
A. $ 14:15 $
B. $ 6:35 $
C. $ 41:32 $
D. $ 10:21 $

Hint: The ratio of two quantities signifies the number of times one quantity is to the other quantity. For example, if the ratio of mass of body A to the mass of body B is $ 1:2 $ , it means the mass of body B is two times the mass of body A. Use the definition of types of ratios to find out how to calculate the compounded ratio.

Complete step-by-step answer:
Types of ratio are –
I.Duplicate ratio -
When a ratio is compounded of itself, the resultant ratio is called a duplicate ratio.
For example- When $ a:b $ is compounded to itself we get $ {a^2}:{b^2} $ .
Thus, the ratio obtained is the duplicate ratio.
II.Triplicate ratio -
When a duplicate ratio is further compounded with its parent ratio, the resultant ratio is called the triplicate ratio.
For example- When $ {a^2}:{b^2} $ is compounded with its parent ratio that is $ a:b $ , the resultant ratio is $ {a^3}:{b^3} $ . Thus the ratio obtained is the triplicate ratio.
So keep in mind the definition of all the types of ratios to get the correct answers.
III.Compound ratio:
Term wise multiplication of the two ratios that is the antecedent of one ratio multiplied with the antecedent of the other ratio gives the antecedent of the compound ratio and same goes with the consequences of the ratio.
For example- The compound ratio of $ a:b $ and $ c:d $ is $ ac:bd $ .
So the compound ratio of $ 2:3 $ and $ 5:7 $ is,
 $
\Rightarrow 2 \times 5:3 \times 7 \\
\Rightarrow 10:21 \;
  $
Hence, option (D) is the correct answer.
So, the correct answer is “Option D”.

Note: We can calculate the compound ratio of two or more than two ratios.
For example, the compound ratio of $ a:b $ , $ c:d $ and $ e:f $ is $ ace:bdf $. This concept can be applied to any number of ratios.