The ratio of 45% of 80% of A to 30% of 40% of B is 15 : 4. If the average of A and B is 67.5, what is the value of (A - B)?

The ratio of 45% of 80% of A to 30% of 40% of B is 15 : 4.

$$\frac{45\%\ of\ 80\%\ of\ A}{30\%\ of\ 40\%\ of\ B}\ =\ \frac{15}{4}$$

$$\frac{\frac{45}{100}\times\frac{80}{100}\times A}{\frac{30}{100}\times\frac{40}{100}\times B}\ =\ \frac{15}{4}$$

$$\frac{45\times80\times A}{30\times40\times B}\ =\ \frac{15}{4}$$

$$\frac{A}{B}\ =\frac{5}{4}$$

Let's assume A = 5y and B = 4y.    Eq.(i)

If the average of A and B is 67.5.

$$\frac{A+B}{2}\ =\ 67.5$$

A+B = 135

Put Eq.(i) in the above equation.

5y+4y = 135

9y = 135

y = 15

Value of (A - B) = (5y-4y) = y = 15