If p : q = 2/3 : 5/6 and q : r = 3/4 : 1/2, find p : q : r
A.
12 : 15 : 10
B.
12 : 15 : 16
C.
10 : 15 : 24
D.
9 : 10 : 15
Correct Answer: 12 : 15 : 10
Explanation
If p : q = 2/3 : 5/6, then the sum S1 of ratio = 2/3 + 5/6 = 9/6
If q : r = 3/4 : 1/2, then the sum S2 of ratio = 3/4 + 1/2 = 5/4
Let p + q = T1, then
q = (5/6÷9/6)T1 = (5/6×6/9)T1 = 5/9T1
Again, let q + r = T2, then
q = (3/4÷5/4)T2 = (3/4×4/5)T2 = 3/5T2
Using q = q
5/9T1 = 3/5T2
5 x 5T1 = 9 x 3T2
T1/T2 = 9×3/5x5 = 27/25
Giving that, T1 = 27 and T2 = 25
P = (2/3÷S1)T1 = (2/3÷9/6)T1
= (2/3×6/9)27 = 12
q = (5/6÷S1)T1 = (5/6÷9/6)T1
= (5/6×6/9)27 = 15
and r = (1/2÷S2)T2 = (1/2÷5/4)T2
= (1/2×4/5)25 = 10
Hence p : q : r = 12: 15 : 10
If p : q = 2/3 : 5/6, then the sum S1 of ratio = 2/3 + 5/6 = 9/6
If q : r = 3/4 : 1/2, then the sum S2 of ratio = 3/4 + 1/2 = 5/4
Let p + q = T1, then
q = (5/6÷9/6)T1 = (5/6×6/9)T1 = 5/9T1
Again, let q + r = T2, then
q = (3/4÷5/4)T2 = (3/4×4/5)T2 = 3/5T2
Using q = q
5/9T1 = 3/5T2
5 x 5T1 = 9 x 3T2
T1/T2 = 9×3/5x5 = 27/25
Giving that, T1 = 27 and T2 = 25
P = (2/3÷S1)T1 = (2/3÷9/6)T1
= (2/3×6/9)27 = 12
q = (5/6÷S1)T1 = (5/6÷9/6)T1
= (5/6×6/9)27 = 15
and r = (1/2÷S2)T2 = (1/2÷5/4)T2
= (1/2×4/5)25 = 10
Hence p : q : r = 12: 15 : 10
