Home » 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}) :…

If p : q = (frac{2}{3}) : (frac{5}{6}) and q : r = (frac{3}{4}) : (frac{1}{2}), find p : q : r
• A.
12 : 15 : 10
• B.
12 : 15 : 16
• C.
10 : 15 : 24
• D.
9 : 10 : 15
##### 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