Question

The triplicate ratio of 4:7 is _ _ _ _
\[
  \left( A \right)49:16 \\
  \left( B \right)64:343 \\
  \left( C \right)16:49 \\
  \left( D \right)\sqrt[3]{4}:\sqrt[3]{7} \\
 \]

Answer 1

Hint: In this question, we use the concept of triplicate ratio. The triplicate ratio is the compound ratio of three equal ratios. The triplicate ratio of the ratio a: b is the ratio ${a^3}:{b^3}$ .In other words, the triplicate ratio of the ratio a: b is the compound ratio of a:b, a:b and a:b.

Complete Step-by-Step solution:
Given, we have a ratio 4:7.
Now, we have to find the triplicate ratio of 4:7 so in the triplicate ratio we have to find the compound ratio of 4:7, 4:7 and 4:7.
In compound ratio two or more ratios are multiplied term wise. For example: The compounded ratio of the two ratios a: b and c: d is the ratio ac: bd, and that of a: b, c: d and e: f is the ratio ace: bdf.
Now, the triplicate ratio of 4:7 is ${4^3}:{7^3}$
$ \Rightarrow 64:343$
The triplicate ratio of 4:7 is $64:343$
So, the correct option is (B).

Note: In such types of problems we have to use the definition of triplicate and compound ratio. We can solve above problem by different way like if a ratio m: n then the triplicate ratio of m: n is $\left( {m \times m \times m} \right):\left( {n \times n \times n} \right)$ . To easily find the triplicate ratio so we have to remember a cube of 1 to 10 numbers.