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 ?

15

Given :-

Ratio of 45% of 80% of A to 30% of 40% of B is 15 : 4

Now , 45% of 80% of A = \(\frac{45}{100}\) × \(\frac{80}{100}\) × A

30% of 40% of B = \(\frac{30}{100}\) × \(\frac{40}{100}\) × B

According to Question ,

\(\frac{45 × 80 × A}{30 × 40 ×B  }\) = \(\frac{15}{4}\)

\(\frac{A}{B}\) = \(\frac{3}{4}\)

A  :  B = 5 : 4

Average of A and B = 67.5

Sum of A and B = 67.5 ×2 = 135

Now , 9R = 135

1R = 15

Difference of A and B = 5R - 4R = 1R

= 15