If p : q = (frac{2}{3}) : (frac{5}{6}) and q : r = (frac{3}{4}) :…

If p : q = (frac{2}{3}) : (frac{5}{6}) and q : r = (frac{3}{4}) : (frac{1}{2}), find p : q : r

Correct Answer: Option A

Explanation

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