The ratio of the ages of a mother and a daughter after 20 years will be 15 : 8 and the ration of their ages 8 years ago was 8 : 1. What is the ratio of their current ages?
Given: Ratio of ages of a mother(M) and a daughter(D) after 20 years = 15 : 8 Ratio of ages of a mother(M) and a daughter(D) 8 years ago = 8 : 1 Calculation: According to question, (M + 20)/(D + 20) = 15/8 8 × (M + 20) = 15 × (D + 20) 8M + 160 = 15D +300 8M – 15D = 300 – 160 8M – 15D = 140 ----(i) (M – 8)/(D – 8 ) = 8 M – 8 = 8 × (D – 8) M – 8 = 8D – 64 M – 8D = 8 – 64 M – 8D = – 56 ----(ii) After multiplying equation (ii) by 8 and subtracting it from equation (i), we get 8 × (M – 8D) – (8M – 15D)= 8 × (– 56) – 140 8M – 64D – 8M + 15D = – 448 – 140 – 49D = – 588 D = 588 / 49 D = 12 And M – 8D = – 56 M – 8 × 12 = – 56 M = 96 – 56 M = 40 Ratio of their present ages = M/D = 40/12 ∴ The ratio of their present ages is 10 : 3.