Ratio P6 2009 SA2 P2 Nanyang Q12

Given that p : (q + r) = 1 : 3, r : (q + s) = 1 : 2 and p : s = 2 : 5.
(a) Find p : q : r : s.
(b) Find (r + q) : (p + s).

                   x 3
p : s = 2 : 5 = 6 : 15

                           x 2       x 3 
p : (q + r) = 1 : 3 = 2 : 6 = 6 : 18

                                            x 3
s + (q + r) = 5 + 6 = 11 ............... 33

                          x 11 
r : (q + s) = 1 : 2 = 11 : 22

s = 15, (q + s) = 22, so q = 22 - 15 = 7

a) p : q : r : s = 6 : 7 : 11 : 15

b) (r + q) : (p + s) = (11 + 7) : (6 + 15)
                             = 18 : 21
                             = 6 : 7