Explanation:

- To solve the problem, set up the equation using the given ratio:

$$

\frac{0.45 \times 0.80 \times A}{0.30 \times 0.40 \times B} = \frac{15}{4}

$$

- Simplify it to:

$$

\frac{0.36A}{0.12B} = \frac{15}{4}

$$

- Further simplify to obtain:

$$

\frac{3A}{B} = \frac{15}{4}

$$

- Cross-multiply to get:

$$

12A = 15B

$$

- The average of A and B is 67.5, which gives:

$$

\frac{A + B}{2} = 67.5 \quad \Rightarrow \quad A + B = 135

$$

- Solve the equations \(12A = 15B\) and \(A + B = 135\):

- From \(12A = 15B\), find \(A = \frac{5}{4}B\)

- Substitute in \(A + B = 135\):

$$

\frac{5}{4}B + B = 135 \quad \Rightarrow \quad \frac{9}{4}B = 135 \quad \Rightarrow \quad B = 60

$$

- Now find A:

$$

A = \frac{5}{4} \times 60 = 75

$$

- Therefore, the value of \(A - B = 75 - 60 = 15\).

- Option:4, 15 is the correct answer.

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