Question

The ratio of present ages of a and b is 3:2 five year ago the ratio of their ages was 5 : 3 that is present age of A?

Answer 1

$\sf\large\underline{Let:}$

$\tt{\implies Their\:present\:age\:be\:x}$

$\tt{\implies Present\:age\:A=3x}$

$\tt{\implies Present\:age\:B=2x}$

$\sf\large\underline{To\: Find:}$

$\tt{\implies Present\:age\:A=?}$

$\sf\large\underline{Given:}$

• The ratio of present ages of a and b is 3:2 five year ago the ratio of their ages was 5 : 3]

$\sf\large\underline{According\:to\:the\: Question:}$

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

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

$\tt{\implies 9x-15=10x-25}$

$\tt{\implies 10x-9x=-15+25}$

$\tt{\implies x=10}$

$\sf\large{Hence,}$

$\tt{\implies Present\:age\:A=3x}$

$\tt{\implies Present\:age\:A=3(10)}$

$\tt{\implies Present\:age\:A=30\: years}$

$\rm{\underbrace{Answer-30\:years}}$

Answer 2

Given :

• The ratio of present ages of A & B is 3:2.
• 5 years ago , the ratio of their ages was 5:3.

To find :

• Present age of A .

Solution :

Consider,

• Present age of A = 3x years
• Present age of B = 2x years

${\underline{\sf{According\:to\:the\: question:-}}}$

• 5 years ago, the ratio of their ages was 5:3.

5 years ago,

• Age of A = (3x -5) years
• Age of B = (2x-5) years

$\mapsto\sf{(3x-5):(2x-5)=5:3}$

$\mapsto\sf{\dfrac{3x-5}{2x-5}=\dfrac{5}{3}}$

$\mapsto\sf{10x-25=9x-15}$

$\mapsto\sf{10x-9x=25-15}$

$\mapsto\sf{x=10}$

• Present age of A = 3 × 10 = 30 years