Question

Q1. The ratio of ages of two persons A and B are 7:9. Twelve years ago, there ages were in the ratio 3:5. When would be the ratio of their ages 6:7?
Q2. If secA+tanA=p show that p^2-1/p^2+1= sinA

Answer 1

$(1) \frac{a}{b} = \frac{7}{9} \\ a = \frac{7}{9} b \\ \frac{a - 12}{b - 12} = \frac{3}{5} \\ \frac{ \frac{7b}{9} - 12 }{b - 12} = \frac{3}{5} \\ 5(7b - 108) = 3 \times 9(b - 12) \\ 35b - 540 = 27b - 324 \\ 8b = 216 \\ b = 27 \\ a = 7 \times 27 \div 9 = 21 \\ after \: x \: years \\ \frac{a + x}{b + x} = \frac{6}{7} \\ 7(21 + x) = 6(27 + x) \\ 147 + 7x = 162 + 6x \\ x = 15$