Question

The age of Aqib and Sa Sania are in the ratio of 1 : 2. After 11 years the ratio in ages will be 2:3. Find their present age

Answer 1

Given,

• The ages of Aqib and Sania are in the ratio of 1:2.
• After 11 years the ratio in ages will be 2:3.

To Find,

• The Present age of Aqib.
• The Present age of Sania.

Solution :

$\implies$ Suppose the age of Aqib and Sania be a years

$\mapsto \underline{\sf{\pink{According \ to \ the \ First \ Condition :}}}$

• The ages of Aqib and Sania are in the ratio of 1:2.

$\implies \sf{The \ Present \ age \ of \ the \ Aqib = a \ years}$

$\implies \sf{The \ Present \ age \ of \ the \ Sania = 2a \ years}$

$\mapsto \underline{\sf{\pink{According \ to \ the \ Second \ Condition :}}}$

• After 11 years the ratio in ages will be 2:3.

$\implies \sf{a + 11 : 2a + 11 = 2:3}$

$\implies \sf{\dfrac{a + 11}{a + 11} = \dfrac{2}{3}}$

$\implies \sf{3(a + 11) = 2(b + 11)}$

$\implies \sf{3a + 33 = 2a + 22}$

$\implies \sf{3a - 2a = 22 - 33}$

$\implies \sf{3a - 2b = 11}$

$\implies \boxed{\sf{a = 11}}$

Therefore,

$\boxed{\large{\sf{\red{The \ Age \ of \ Aqib = a = 11 \ years}}}}$

$\boxed{\large{\sf{\red{The \ Age \ of \ Sania = 2a = 2(11) = 22 \ years}}}}$

$\rule{200}2$

Answer 2

Answer:

Let the Present Age of Aquib and Sania be n and 2n respectively.

$\underline{\bigstar\:\textbf{According to the Question :}}$

$:\implies\sf \dfrac{Aquib+11\:yrs}{Sania+11\:yrs}=\dfrac{2}{3}\\\\\\:\implies\sf \dfrac{n + 11\:yrs}{2n + 11\:yrs} = \dfrac{2}{3}\\\\\\:\implies\sf (n + 11\:yrs)3 = 2(2n + 11\:yrs)\\\\\\:\implies\sf 3n + 33\:yrs = 4n + 22\:yrs\\\\\\:\implies\sf 33\:yrs - 22\:yrs = 4n - 3n\\\\\\:\implies\underline{\boxed{\sf n = 11\:yrs}}$

$\rule{150}{1}$

$\underline{\bigstar\:\textbf{Present Age :}}$

$\bullet\:\:\textsf{Aquib = n = \textbf{11 years}}\\\\\bullet\:\:\textsf{Sania = 2n = 2(11) = \textbf{22 years}}$

⠀

$\therefore\:\underline{\textsf{Aquib \& Sania present age is \textbf{11 \& 22 yrs} respectively}}.$