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.

“”