Two numbers are in the ratio of 5 : 7. If 6 be added to each, the ratio becomes 3 : 4. Find the numbers.

30, 42 55, 88 10, 16 25, 40

30, 42

5   :   7   3   :   4 _________  +6    +6 ATQ, \(\frac{5R\;+\;6}{7R\;+\;6}\) = \(\frac{3}{4}\) Using cross - multiplication, 21R - 20R = 6 x 4 - 6 x 3 ⇒ 1R = 6 Therefore, the numbers are 6 x 5, 6 x 7 = 30, 42