Question

The age of A is five years more than that of B. 5 years ago, the ratio oftheir ages was 3:2. Find their present ages.

Answer 1

$\huge{\underline{\purple{\rm{Solution:}}}}$

$\large{\underline{\red{\rm{Let:}}}}$

• $\rm{The\: present\:age\:of\:A=x}$
• $\rm{The\: present\:age\:of\:B=y}$

$\large{\underline{\red{\rm{Given:}}}}$

• The age of A is five years more than that of B. 5 years ago, the ratio oftheir ages was 3:2

$\large{\underline{\red{\rm{To\: Find:}}}}$

• $\rm{The\: present\:age\:of\:A\:and\:B}$

$\rm\purple{According\:to\:the\: question}$

$\rm{The\:age\:of\:A\:is\:5\: years\: more\:than\:5}$

$\rm{\implies x=y+5}$

$\rm\green{\implies x-y=5-----(i)}$

$\rm{5\: years\:ago\:the\: ratio\:of\: their\:age\:was\:3:2}$

$\rm{\implies \dfrac{x-5}{y-5}=\dfrac{3}{2}}$

$\rm{\implies 2(x-5)=3(y-5)}$

$\rm{\implies 2x-10=3y-15}$

$\rm{\implies 2x-3y=-15+10}$

$\rm\green{\implies 2x-3y=-5------(ii)}$

• $\rm{Solving\: equation\:1\:and\:2}$

$\rm{\implies x-y=5}$

$\rm{\implies 2x-3y=-5}$

• $\rm{in\:eq\:1\: multiplying\:by\:2\:than\: subtract}$

$\rm{\implies 2x-2y=10}$

$\rm{\implies 2x-3y=-5}$

• $\rm{by\: solving\: equation\:we\:get\:here}$

$\rm{\implies y=15}$

$\rm\red{\implies y=15}$

• $\rm{putting\:the\: value\:y=15\:in\:eq\:1}$

$\rm{\implies x-y=5}$

$\rm{\implies x-15=5}$

$\rm{\implies x=5+15}$

$\rm\red{\implies x=20}$

Hence,

$\rm{The\: present\:age\:of\:A=20\: year's}$

$\rm{The\: present\:age\:of\:B=15\: year's}$