Two numbers are in the ratio of 11: 19. If each one is subtracted by 7, then the ratio of the new numbers becomes 5:9. Find the absolute difference between the actual numbers.

Correct option is B

​Given:

Two numbers are in ratio 11:19

Subtract 7 from each, the ratio becomes 5:9

Solution:

Let the numbers be 11x and 19x
 Subtracting 7:

$$\frac{11x - 7}{19x - 7} = \frac{5}{9}$$​​

​$$9(11x - 7) = 5(19x - 7) \\ \ \\ 99x - 63 = 95x - 35 \\ \ \\ 99x - 95x = 63 - 35$$​​

​$$4x = 28\\ \ \\ \implies x = 7$$​​

Numbers are:

​$$11x= 11\times7 = 77, \, \\ \ \\ 19x = 19\times7= 133$$​​

Absolute difference:

= 133 - 77 = 56