If \(p : q = \frac{2}{3} : \frac{5}{6}\) and \(q :... | JAMB UTME - Mathematics - 2010

Question 1 Report

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

12 : 15 : 10

12 : 15 : 16

10 : 15 : 24

9 : 10 : 15

Answer Details

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

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