Question

3. (a) The present ages of a father and his son are in the ratio 10:3. If the son is 15 years old now, in how many years will the ratio of their ages be 2:1?
(b) The arithmetic mean of x, y and z is 6 while that of x, y, z, t, u and 9. Calculate the arithmetic mean of t, u, v and w.

Accepted Answer

(a) Father/Son = 10/3 = x/15, so x = (10×15)/3 = 50 years (father's present age). Let a = number of years after which ratio becomes 2:1: (50+a)/(15+a) = 2/1. Cross-multiply: 15+a×2 = 50+a ⇒ 30+2a=50+a ⇒ a = 20 years. Check: (50+20)/(15+20) = 70/30 = 2:1 ✓.

(b) Arithmetic mean of x,y,z is 6, so x+y+z=18 (i). Arithmetic mean of x,y,z,t,u,v,w is 9 (7 quantities), so x+y+z+t+u+v+w=63. Substituting (i): 18+t+u+v+w=63, so t+u+v+w=45. Average of t,u,v,w = 45/4 = 11.25.

WAEC Mathematics 2013 Theory — Question 3

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