Theory question 103
Ratio, Percentages and Rates(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, v and w is 9. Calculate the arithmetic mean of t, u, v, and w.
Show the model answer
Model answer
(a) Father = 15 × 10/3 = 50. (50 + n)/(15 + n) = 2 → 50 + n = 30 + 2n → n = 20 years.
(b) x + y + z = 18 and the seven numbers total 7 × 9 = 63. t + u + v + w = 45, so their mean = 45/4 = 11.25.
Explanation
Turn each mean back into a total first.