The ratio of present ages of R and Q is 5:7, respectively. The difference between the ages of R and Q is ____ years, and the ratio of their ages after 10 years will be ____. Which of the following options can be used to fill the blank in order to make the given statement true?
I. 4, 5:6
II. 8, 15:19
III. 2, 15:17
IV. 10, 7:10

ATQ, Let, present ages of R and Q be ‘5x’ years and ‘7x’ years, respectively. Difference in ages = 7x – 5x = 2x years Option I: 2x = 4 x = 2 Ratio of ages after 10 years = (10 + 10):(14 + 10) = 20:24 = 5:6 Option I can be the answer. Option II: 2x = 8 x = 4 Ratio of ages after 10 years = (20 + 10):(28 + 10) = 30:38 = 15:19 Option II can be the answer. Option III: 2x = 2 x = 1 Ratio of ages after 10 years = (5 + 10):(7 + 10) = 15:17 Option III can be the answer. Option IV: 2x = 10 x = 5 Ratio of ages after 10 years = (25 + 10):(35 + 10) = 35:45 = 7:9 Option IV can’t be the answer.