Mathematics 2010 JAMB Past Questions - Question 6: If p:q=2/3 :5/6 and q:r=3/4:1/2 ,find p:q:r .

Correct Answer

C

Explanation

P : q = â…” : â…š → p = â…”, q=â…š q : r ¾ : ½ → q = ¾ , r = ½ q =â…š , q = ¾ i.e q = â…š X ¾ = 5/8 i.e p : q : r = â…” : 5/8 :½ = 16 : 15 : 12/24 = 12: 15: 16To find the ratio p:q:r, we need to combine the given ratios p:q and q:r.Given:p:q = 2/3 : 5/6q:r = 3/4 : 1/2To combine these ratios, we need to make the middle term (q) the same in both ratios. We can do this by multiplying the first ratio by 2/2 and the second ratio by 3/3:p:q = (2/3) * (2/2) : (5/6) * (2/2)    = 4/6 : 10/12    = 4/6 : 5/6q:r = (3/4) * (3/3) : (1/2) * (3/3)    = 9/12 : 3/6    = 9/12 : 6/12Now, we can combine the ratios:p:q:r = 4/6 : 5/6 : 9/12 : 6/12To simplify the ratio, we can find the least common denominator (LCD) of the fractions involved, which is 12:p:q:r = (4/6) * (2/2) : (5/6) * (2/2) : (9/12) * (1/1) : (6/12) * (1/1)      = 8/12 : 10/12 : 9/12 : 6/12Now, we can express the ratio in its simplest form:p:q:r = 12 : 15 : 10. Therefore, the ratio p:q:r is 2/3 : 12 : 15 : 10.