Question

Tick (✓) the correct answer:
The ages of A and B are in the ratio 5 : 7. Four years from now the ratio of their ages will be 3 : 4. The present age of B is
(a) 20 years
(b) 28 years
(c) 15 years
(d) 21 years

Answer 1

(b) 28 years

$$\begin{gathered} \mathrm{Let}\mathrm{x}\mathrm{be}\mathrm{the}\mathrm{common}\mathrm{multiple}\mathrm{of}\mathrm{the}\mathrm{ages}\mathrm{of}\mathrm{A}\mathrm{and}\mathrm{B}. \\ \mathrm{Then}.\mathrm{the}\mathrm{age}s\mathrm{of}\mathrm{A}\mathrm{and}\mathrm{B}\mathrm{would}\mathrm{be}5\mathrm{x}\mathrm{and}7\mathrm{x},\mathrm{respectively}. \\ \therefore \frac{5x+4}{7x+4}=\frac{3}{4} \\ \Rightarrow 4(5x+4)=3(7x+4) \\ \Rightarrow 20x+16=21x+12 \\ \Rightarrow 16-12=21x-20x \\ \Rightarrow 4=x \\ \Rightarrow x=4 \\ \therefore \mathrm{Age}\mathrm{of}B=7\left(x\right)=7\times 4 \\ =28\mathrm{years} \end{gathered}$$