Question

The ratio of the ages of a father and son is 17:7, respectively. Six years ago the ratio of their ages was 3:1, respectively. What is the son’s present age? (Answer: 21 years)​

Answer 1

Answer:

Given :-

• The ratio of the ages of a father and son is 17 : 7.
• Six years ago the ratio of their ages was 3 : 1 respectively.

To Find :-

• What is the present age of son's.

Solution :-

Let,

$\mapsto$ Present age of father be 17x years

$\mapsto$ Present age of son will be 7x years

Six years ago :

$\leadsto$ Age of father = 17x - 6 years

$\leadsto$ Age of son = 7x - 6 years

According to the question,

$\implies \sf \dfrac{17x - 6}{7x - 6} =\: \dfrac{3}{1}$

By doing cross multiplication we get,

$\implies \sf 3(7x - 6) =\: 1(17x - 6)$

$\implies \sf 21x - 18 =\: 17x - 6$

$\implies \sf 21x - 17x =\: - 6 + 18$

$\implies \sf 4x =\: 12$

$\implies \sf x =\: \dfrac{\cancel{12}}{\cancel{4}}$

$\implies \sf\bold{\purple{x =\: 3\: years}}$

Hence, the required ages of father and son are :

$\dashrightarrow$ Present age of father :

$\Rightarrow \sf 17x\: years$

$\Rightarrow \sf 17(3)\: years$

$\Rightarrow\sf 17 \times 3\: years$

$\Rightarrow\sf\bold{\green{51\: years}}$

And,

$\dashrightarrow$ Present age of son :

$\Rightarrow \sf 7x\: years$

$\Rightarrow \sf 7(3)\: years$

$\Rightarrow \sf 7 \times 3\: years$

$\Rightarrow\sf\bold{\red{21\: years}}$

$\therefore$ The present age of son is 21 years.

$\rule{150}{2}$

#Learn more :

Ava and Liam's ages are currently in a ration of 4:5 respectively. After 5 years, their ages would be in a ration of 5:6 respectively. What is Ava's current age?

https://brainly.in/question/36660654

Answer 2

$\bf\underline{\underline{\red{★Question:-}}}$

The ratio of the ages of a father and son is 17:7, respectively. Six years ago the ratio of their ages was 3:1, respectively. What is the son’s present age?

$\bf\underline{\underline{\red{★Given:-}}}$

•The ratio of the ages of a father and son is 17:7, respectively. •Six years ago the ratio of their ages was 3:1, respectively.

$\bf\underline{\underline{\red{★To \: find:-}}}$

•His Son's present age.

$\bf\underline{\underline{\red{★Solution:-}}}$

Let, his father's present age be 17x.

And, son's present age be 7x.

•6 years before his father's age should be 17x - 6.

•And 6 years ago his son's age should be 7x - 6.

$\bf\underline{\underline{\red{★Applying \: condition:-}}}$

$\frac{17x - 6}{7x - 6} = \frac{3}{1}$

By cross-multiplication:-

$1(17x - 6) = 3(7x - 6)$

By multiplying:-

$→17x - 6 = 21x - 18$

By transforming to LHS and RHS:-

$→21x - 17x = - 6 + 18$

Solving them:-

$→4x = 12$

Transforming 4 to RHS:-

$→x = \frac{12}{4}$

Solving them:-

$→x = 3$

Therefore,

•Father's present age = 17x

= 17×3 = 51 years

•Son's present age = 7x = 7×3 = 21 years.

★Hence, their son's age = 21 years.