question_answer

Present age of father is 42 years and that of his son is 14 years. 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 years old.

(c) Age of father after 10 years to the age of son after 10 years.

(d) Age of father to the age of son when father was 30 years old.

Answer:

Present age of father = 42 years

Present age of son = 14 years

(a) Ratio of present age of father to the present age of son

\[=42\text{ }years:14\text{ }years\]

\[=42:14=\frac{42}{14}=\frac{3}{1}\]

\[=3:1\]

(b) When son?s was 12 years that means 2 years ago.

Then the father?s age \[=(422)\text{ }years\]

\[=40\text{ }years\].

Required Ratio \[=40:12=\frac{40\div 4}{12\div 4}=\frac{10}{3}\]

\[=10:3\]

(c) After 10 years:

Father?s age \[=(42+10)\text{ }years\]

\[=52\text{ }years\]

Son?s age \[=(14+10)\text{ }years\]

\[=24\text{ }years\]

\[\therefore \] Required Ratio \[=52\text{ }years:24\text{ }years\]

\[=52:24\]

\[=\frac{52}{24}=\frac{52\div 4}{24\div 4}=\frac{13}{6}\]

\[=13:6\]

(d) When father?s age is 30 years (that mean 12 years ago) so the son?s age

\[=1412=2\text{ }years\]

\[\therefore \]  Required Ratio \[=30\text{ }years:2\text{ }years\]

\[=30:2=\frac{30}{2}=\frac{15}{1}\]

\[=15:1\]