• question_answer 16) Present age of father is 42 yr and that of his son is 14 yr. Find the ratio of (a) present age of father to the present age of son. (b) age of the father to the age of son, when son was 12 yr old. (c) age of father after 10 yr to the age of son after 10 yr. (d) age of father to the age of son when father was 30 yr old.

Given, present age of father = 42 yr and present age of son = 14 yr (a) Required ratio $\text{=}\frac{\text{Present}\,\text{age}\,\text{of}\,\text{father}}{\text{Present}\,\text{age}\,\text{of}\,\text{son}}=\frac{42yr}{14yr}=\frac{42}{14}$ $=\frac{42\div 14}{14\div 14}=\frac{3}{1}=3:1$ [$\because$HCF of 42 and 14 = 14] (b) When son's age was 12 yr i.e. 2 yr back (because son's present age is 14 yr), then father's age = (42 ? 2) = 40 yr $\therefore$ Required ratio $=\frac{2yr\,back\,father's\,age}{2yr\,back\,son's\,age}=\frac{40yr}{12yr}=\frac{40}{12}=\frac{40\div 4}{12\div 4}$ $\because$$40=2\times 2\times 2\times 5$ and $12=2\times 2\times 3$ $\therefore$ HCF of 40 and $12=2\times 2=4=\frac{10}{3}=10:3$ (c) After 10 yr father and son's age will be (42 + 10) yr and (14 + 10) yr respectively i.e. 52 yr and 24 yr. $\therefore$ Required ratio $\text{=}\frac{\text{After}\,\text{10yr}\,\text{father }\!\!'\!\!\text{ sage}}{\text{After}\,\text{10yr}\,\text{son }\!\!'\!\!\text{ s}\,\text{age}}=\frac{52yr}{24yr}=\frac{52\div 4}{24\div 4}$                 $\because$ $52=2\times 2\times 13$ and $24=2\times 2\times 2\times 3$ $\therefore$ HCF of 52 and $24=4=\frac{13}{6}=13:6$ (d) When father's age was 30 yr i.e. 12 yr back (because father's present age is 42 yr and (42 ? 12) = 30 yr. Then, son's age = (14 ? 12) = 2 yr Required ratio $=\frac{\text{12 yr back father }\!\!'\!\!\text{ s age }}{\text{12 yr back son s age}}$ $=\frac{30yr}{2yr}=\frac{30}{2}$$=\frac{30\div 2}{2\div 2}=\frac{15}{1}=15:1$ [$\because$HCF of 30 and 2 = 2]