JAMB Mathematics 2010 Paper

Concept:To combine two ratios, make the common term $q$ equal in both ratios.Explanation:Given $p : q = \frac{2}{3} : \frac{5}{6}$.Multiply both parts by 6 to remove fractions: $p : q = 4 : 5$.Also, $q : r = \frac{3}{4} : \frac{1}{2}$.Multiply both parts by 4: $q : r = 3 : 2$.In the first ratio, $q = 5$.In the second ratio, $q = 3$.The LCM of 5 and 3 is 15.Scale the first ratio so that $q = 15$: $4 : 5 = 12 : 15$.Scale the second ratio so that $q = 15$: $3 : 2 = 15 : 10$.Since $q = 15$ in both ratios, combine them directly:$p : q : r = 12 : 15 : 10$.Answer:$p : q : r = 12 : 15 : 10$, so the correct option is A.