Question

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?
1. 5 : 2
2. 23 : 14
3. 4 : 1
4. 10 : 3

Answer 1

Correct Answer - Option 4 : 10 : 3

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.