Question

Present age of Abhiram is 7 times of his son's age.5 years later the product of their ages is 297 .Find their ages.​

Answer 1

Answer:-

$\large{\boxed{\star{\mathfrak\green{Present \: age \: of \: Abhiram = 28 \: years}}}}$

$\large{\boxed{\star{\mathfrak\blue{Present \: age \:of \: his \: son = 4 \: years}}}}$

Step-by-step explanation:-

Given:-

• Present age of Abhiram = 7 times his son's age.

• 5 years later, their product of ages =297

To find:-

• Their present ages = ?

Let present age of his son be x years.So present age of Abhiram = 7x years.

A/Q,

$\implies\tt (x+5) \times (7x+5)= 297 \\\\\\\implies\tt {7x}^{2} + 5x + 35x + 25 = 297 \\\\\\\implies\tt 7{x}^{2} + 40x + 25 = 297 \\\\\\\implies\tt {7x}^{2} + 40x + 25 - 297 = 0 \\\\\\\implies\tt {7x}^{2} + 40x - 272 = 0 \\\\\\\implies\tt {7x}^{2} - 28x + 68x - 272 = 0 \\\\\\\implies\tt 7x(x - 4) + 68(x - 4) = 0 \\\\\\\implies\tt (7x + 68) (x - 4) = 0 \\\\\\\implies\tt (7x + 68) = 0 \: \: \: or \: \: \: (x - 4) = 0 \\\\\\\implies\tt 7x = - 68 \: \: \: or, \: \: \: x = 4 \\\\\\\tt \: \: [\because Age \neq Negative]\\\\\\\therefore\large\sf\green{x = 4 }$

$\rule{200}{1}$

Ages :-

${\underline{\star{\sf\green{Age \: of \: Abhiram :-}}}}$

$\rightarrow\sf 7x = 7(4)$ = ${\boxed{\sf\green{28 \: years }}}$

${\underline{\star{\sf\pink{Age \: of \: his \: son :- }}}}$

$\rightarrow\sf x$ = ${\boxed{\sf\green{ 4 \: years}}}$

Answer 2

AnsweR :

$\bf{\Large{\underline{\sf{Given\::}}}}$

Present age of Abhiram is 7 times of his son's age. 5 years later the product of their ages is 297.

$\bf{\Large{\underline{\sf{To\:find\::}}}}$

Their ages.

$\bf{\Large{\underline{\tt{\purple{Explanation\::}}}}}$

Let the present age of son be R years

Let the present age of Abhiram be 7R years.

A/q

$\bf{\Large{\boxed{\rm{After\: 5\:years\::}}}}}}$

$\leadsto\sf{The\:son\:age\:=\:(R+5)\:years}\\\\\leadsto\sf{The\:Abhiram\:age\:=\:(7R+5)\:years}$

So,

$|\implies\sf{(R+5)(7R+5)=297}\\\\\\|\implies\sf{7R^{2} +5R+35R+25=297}\\\\\\|\implies\sf{7R^{2} +40R+25=297}\\\\\\|\implies\sf{7R^{2} +40R+25-297=0}\\\\\\|\implies\sf{7R^{2} +40R-272=0}\\\\\\|\implies\sf{7R^{2} -28R+68R-272=0}\\\\\\|\implies\sf{7R(R-4)+68(R-4)=0}\\\\\\|\implies\sf{(R-4)(7R+68)=0}\\\\\\|\implies\sf{R-4=0\:\:\:\:\:Or\:\:\:\:\:\:7R+68=0}\\\\\\|\implies\sf{R\:=\:4\:\:\:\:\:\:Or\:\:\:\:\:7R=-68}\\\\\\|\implies\sf{\red{R\:=\:4\:\:\:\:Or\:\:\:R\:=\:\dfrac{-68}{7} }}$

∴The value is 4 & not negative acceptable.

Thus,

The age of son is R = 4 Years.

The age of Abhiram is 7(4) = 28 years.