Question

12 years ago agr of p was three times the age of q after 12 years ratio of ages of q and p is 2:3 what is present age of p​

Answer 1

AnswEr :

Let the Present Age be p yrs and, q yrs.

• 12 ⠀YEARS ⠀AGO :

◗ p = (p – 12)

◗ q = (q – 12)

• According to the Question Now :

↠ p = 3 times of q ⠀(12 yrs ago)

↠ (p – 12) = 3(q – 12)

↠ p – 12 = 3q – 36

↠ p = 3q – 36 + 12

↠ p = 3q – 24 ⠀⠀⠀⠀— eq.( I )

_______________________________

• 12 ⠀YEARS ⠀FROM ⠀NOW :

◗ p = (p + 12)

◗ q = (q + 12)

• According to the Question Now :

↠ q : p = 2 : 3 ⠀(12 yrs from now)

↠ (q + 12) : (p + 12) = 2 : 3

• putting the value of p from eq. ( I )

↠ (q + 12) : (3q – 24 + 12) = 2 : 3

↠ (q + 12) : (3q – 12) = 2 : 3

• Product of Extreme = Product of Mean

↠ 3(q + 12) = 2(3q – 12)

↠ 3q + 36 = 6q – 24

↠ 36 + 24 = 6q – 3q

↠ 60 = 3q

• Dividing both term by 3

↠ q = 20 years

━━━━━━━━━━━━━━━━━━━━━━━━

• Putting value of q in eq. ( I ) :

⇒ p = 3q – 24

⇒ p = 3(20) – 24

⇒ p = 60 – 24

⇒ p = 36 years

⠀

∴ Hence, Present Age of p is 36 years.

Answer 2

$\bf{\Huge{\boxed{\tt{\blue{ANSWER\::}}}}}$

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

12 years ago age of P was three times the age of Q after 12 years ratio of ages of P & Q is 2:3.

$\bf{\Large{\underline{\bf{To\:Find\::}}}}$

The present age of P.

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

$\bf{\huge{\boxed{\underline{\sf{12\:years\:agO\::}}}}}}$

$\bf{We\:have}\begin{cases}\sf{The\:age\:of\:P\:=\:(P-12)\:years.}\\ \sf{The\:age\:of\:Q\:=\:(Q-12)\:years.}\end{cases}}$

A/q

$\implies\sf{(P-12)=3(Q-12)}$

$\implies\sf{P-12=3Q-36}$

$\implies\sf{P-3Q\:=\:-36+12}$

$\implies\sf{P-3Q\:=\:-24}$

$\implies\sf{P\:=\:-24+3Q........................(1)}$

$\bf{\huge{\boxed{\underline{\sf{After\:12\:years\::}}}}}}$

$\bf{We\:have}\begin{cases}\sf{The\:age\:of\:P\:=\:(P+12)\:years.}\\ \sf{The\:age\:of\:Q\:=\:(Q+12)\:years.}\end{cases}}$

A/q

$\implies\sf{(Q+12)\::\:(P+12)\:=\:2:3}$

$\implies\sf{\frac{Q+12}{P+12} \:=\:\frac{2}{3} }$

$\bf{\large{\boxed{\underline{\bigstar{\tt{Multiplication\::}}}}}}$

$\implies\sf{3(Q+12)=2(P+12)}$

$\implies\sf{3(Q+12)\:=\:2(-24+3Q+12)}$

$\implies\sf{3(Q+12)\:=\:2(3Q-12)}$

$\implies\sf{3Q+36\:=\:6Q-24}$

$\implies\sf{3Q\:-\:6Q\:=\:-24-36}$

$\implies\sf{-3Q\:=\:-60}$

$\implies\sf{Q\:=\:\cancel{\frac{-60}{-3} }}$

$\implies\sf{\red{Q\:=\:20\:years}}$

&

Putting the value of Q in equation (1), we get;

$\implies\sf{P\:=\:-24+3(20)}$

$\implies\sf{P\:=\:-24+60}$

$\implies\sf{\red{P\:=\:36\:years}}$

Thus,

$\bf{\Large{\boxed{\rm{The\:present\:age\:of\:P\:is\:\:\:36\:years.}}}}}$