Question

4 years,hence the ratio of ages of P & Q will be 2:1 and also the sum of their present ages is 46 years.find the present age of P?

Answer 1

Answer:

Let the present age of P be p and present age of Q be q.

Sum of their present ages = 46

= > p + q = 46

= > q = 46 - p

After 4 year, age of P = p + 4 After 4 year, age of Q = q + 4 from above, q = 46 - p

So, age of Q after 4 year = 46 - p + 4 = 50 - p

After 4 year:

= > Ratio of their ages = 2 : 1

= > ( p + 4 ) : ( 50 - p ) = 2 : 1

= > 1( p + 4 ) = 2( 50 - p )

= > p + 4 = 100 - 2p

= > p + 2p = 100 - 4

= > 3p = 96

= > p = 32

Hence the present age of P is 32 year.

Answer 2

$\huge\star \: {\sf{\underline{\orange{SolUtion:-}}}}$

${\tt{\pink{Let\: the \: present \: age\: of \: P \: is\: p \: and \: the \: present\: age\: Q\: is \:q }}}$

${\tt{\pink{Sum \: of \: their \: present \: ages = 46 }}}$

${\implies{\tt{p + q = 46}}}$

${\implies{\tt{q = 46 - p}}}$

${\tt{After \: 4 year \: age\: of \:P = 4+p}}$

${\tt{After ,\: 4 year \: age \: of \: Q= 4+q}}$

${\tt{So, \:age of\: Q \:after\: 4year \: 46 - p + 4 = 50 - p }}$

${\tt{\pink{After\: 4\: year ,}}}$

$\implies{\tt{\blue{ Ratio \: of \: their \: ages = 2 : 1}}}$

$\implies{\tt{\blue{ (P + 4) :(50 - p) = 2:1}}}$

$\implies{\tt{\blue{ 1 (P + 4) : 2(50 - p) }}}$

$\implies{\tt{\blue{P + 4 = 100 -2p}}}$

$\implies{\tt{\blue{ p+2p = 100 - 4}}}$

$\implies{\tt{\blue{ 3p = 96}}}$

$\implies{\tt{\blue{p = 32 }}}$

$\boxed {\green{ \: Hence \: the \: present \: age \: of p \: is \: 32.}}$