Question

The ratio of ages (in years) of 14 and BIO years ago, was 23:12. The ratio of their ages after 15 ve
ye
be 35:24. What is the ratio of present ages of A and B ?​

Answer 1

$\sf Question:$

The ratio of ages (in years) of A and B 9 years ago, was 23:12. The ratio of their ages after 15 years will be 35:24. What is the ratio of present ages of A and B?

$\sf Answer :$

Let the Age of A be 23x and of B be 12x 9 years ago from Present Age.

$\underline{\bigstar\:\textsf{According to the given Question :}}$

$:\implies\sf \dfrac{A+9+15}{B+9+15}=\dfrac{35}{24}\\\\\\:\implies\sf \dfrac{23x+9+15}{12x+9+15}=\dfrac{35}{24}\\\\\\:\implies\sf \dfrac{23x+24}{12x+24}=\dfrac{35}{24}\\\\\\:\implies\sf \dfrac{23x+24}{12(x+2)}=\dfrac{35}{24}\\\\\\:\implies\sf \dfrac{23x+24}{x+2}=\dfrac{35}{2}\\\\\\:\implies\sf (23x + 24) \times 2 = 35 \times (x + 2)\\\\\\:\implies\sf 46x + 48 = 35x + 70\\\\\\:\implies\sf 46x - 35x = 70 - 48\\\\\\:\implies\sf 11x = 22\\\\\\:\implies\sf x = \dfrac{22}{11}\\\\\\:\implies\sf x = 2$

$\rule{180}{1.5}$

$\underline{\bigstar\:\textsf{Required ratio of Present Age of A \& B:}}$

$\dashrightarrow\sf \:\:\dfrac{A}{B}=\dfrac{23x+9}{12x+9}\\\\\\\dashrightarrow\sf \:\: \dfrac{A}{B}=\dfrac{23(2)+9}{12(2)+9}\\\\\\\dashrightarrow\sf \:\: \dfrac{A}{B}=\dfrac{46+9}{24+9}\\\\\\\dashrightarrow\sf \:\: \dfrac{A}{B}=\dfrac{55}{33}\\\\\\\dashrightarrow\sf \:\: \dfrac{A}{B}=\dfrac{5}{3}\\\\\\\dashrightarrow \: \:\underline{\boxed{\sf A:B = 5:3}}$

Answer 2

Answer:

I just need a friend

....................................