If p q frac 2 3 frac 5 6 and q r frac 3 4 frac ... - JAMB Mathematics 2010 Question

If p : q = (\frac{2}{3}) : (\frac{5}{6}), then the sum S₁ of ratio = (\frac{2}{3}) + (\frac{5}{6}) = (\frac{9}{6})

If q : r = (\frac{3}{4}) : (\frac{1}{2}), then the sum S₂ of ratio = (\frac{3}{4}) + (\frac{1}{2}) = (\frac{5}{4})

Let p + q = T₁, then

q = ((\frac{5}{6} \div \frac{9}{6}))T₁ = ((\frac{5}{6} \times \frac{6}{9}))T₁ = (\frac{5}{9})T₁

Again, let q + r = T₂, then

q = ((\frac{3}{4} \div \frac{5}{4}))T₂ = ((\frac{3}{4} \times \frac{4}{5}))T₂ = (\frac{3}{5})T₂

Using q = q

(\frac{5}{9})T₁ = (\frac{3}{5})T₂

5 x 5T₁ = 9 x 3T₂

(\frac{T_1}{T_2}) = (\frac{9 \times 3}{5 x 5}) = (\frac{27}{5})

Giving that, T₁ = 27 and T₂ = 25

P = ((\frac{2}{3} \div S_1))T₁ = ((\frac{2}{3} \div \frac{9}{6}))T₁

= ((\frac{2}{3} \times \frac{6}{9}))27 = 12

q = ((\frac{5}{6} \div S_1))T₁ = ((\frac{5}{6} \div \frac{9}{6}))T₁

= ((\frac{5}{6} \times \frac{6}{9}))27 = 15

and r = ((\frac{1}{2} \div S_2))T₂ = ((\frac{1}{2} \div \frac{5}{4}))T₂

= ((\frac{1}{2} \times \frac{4}{5}))25 = 10

Hence p : q : r = 12: 15 : 10