If 80% of A is 13 more than 90% of B, and the ratio of 40% of A to 60% of B is 10 : 9, then what is the value of A - B ?

20

80% = \(\frac{4}{5}\)  & 90% = \(\frac{9}{10}\)
 
40% = \(\frac{2}{5}\)  &  60%  =  \(\frac{3}{5}\)

80% of A is 13 more than 90% of B

\(\frac{4}{5}\) × A = 13 +  \(\frac{9}{10}\) × B

8A = 130 + 9B

8A - 9B = 130     --------(1)

Now ,

ratio of 40% of A to 60% of B is 10 : 9

\(\frac{2 × A}{3×B}\) = \(\frac{10}{9}\) 

36A = 60B

3A - 5B = 0    -------(2)

Multiply equation (1) by 3 and Equation (2) by 8 . And then subtract them

24A - 27B = 390 & 24A - 40B =0

By subtracting them

13B = 390

B = 30

Put value of B into equation (2)

3A = 30 × 5

3A = 150

A = 50

Now , A - B = 50 - 30 = 20