If p : q = 2/3 : 5/6 and q : r = 3/4 : 1/2, find p : q : r

Correct Answer is : 12 : 15 : 10

Correct Answer is : 12 : 15 : 10

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JAMB Mathematics 2010 Paper

Question : 25

Total: 49

If p : q =

\frac{2}{3}

\frac{5}{6}

\frac{3}{4}

\frac{1}{2}

, find p : q : r

Solution:

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}

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}

Using q = q

\frac{5}{9}

T1 =

\frac{3}{5}

5 x 5T1 = 9 x 3T2

\frac{T_1}{T_2}

\frac{9 \times 3}{5 x 5}

\frac{27}{25}

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

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