Question

The ratio of the present ages of two borthers is 7:9. It the ratio of rheir ages after 4years will be 4:5. Their present ages are-
(a) 20, 40
(b) 28, 36
F
(d) 25,45
(c) 36,28​

Answer 1

Option B.) 28, 36

$\sf{\huge{\underline{\green{Given :-}}}}$

• The ratio of the present ages of two borthers is 7:9.

• The ratio of their ages after 4years will be 4:5.

$\sf{\huge{\underline{\green{To\:Find :-}}}}$

• The present ages .

$\sf{\huge{\underline{\green{Answer :-}}}}$

Let the present ages be x,

According to the question,

The ratio of the present ages of two borthers is 7:9.

So, it will be 7x & 9x

After 4 years,

Ages of them are

• 7x + 4

• 9x + 4

The ratio of their ages will be 4:5.

$\dfrac{7x + 4}{9x + 4} = \dfrac{4}{5}$

➝ 5 (7x + 4) = 4 (9x + 4)

➝ 35x + 20 = 36x + 16

➝ 36x - 35x = 20 - 16

➝ x = 4

Their present ages are 7x & 9x.

• 7x = 7×4 = 28

• 9x = 9 × 4 = 36

Their present ages are 28 & 36.

Answer 2

Answer:

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{orange}{Given:}}}}}}}\end{gathered}$

• ➤ The ratio of the present ages of two borthers is 7:9.
• ➤ The ratio of their ages after 4 years will be 4:5.

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{green}{To Find:}}}}}}}\end{gathered}$

• ➤ Present ages of brothers

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{red}{Solution:}}}}}}}\end{gathered}$

$\dag \: {\underline{\pmb{\frak{\color{purple}{Let \: the \: present \: ages \: of \: borthers \: be \: x}}}}}$

So,

• ⇢ 7x
• ⇢ 9x

$\begin{gathered}\end{gathered}$

$\dag \: \underline{\pmb{\frak{\color{purple}{After \: 4 \: years \: their \: ages \: will \: be \: 4:5.}}}}$

Then, According to the question

$\quad {: \implies{\sf{\dfrac{7x+ 4}{9x + 4} = \dfrac{4}{5}}}}$

• ⇢ By cross multiplication

$\quad {: \implies{\sf{5(7x+ 4)} ={4(9x + 4)} }}$

$\quad {: \implies{\sf{\big[(7x \times 5)+ (4 \times 5)\big]} ={\big[(9x \times 4)+ (4 \times 4)\big]}}}$

$\quad {: \implies{\sf{\big[35x+20\big]} ={\big[36x+ 16)\big]}}}$

$\quad {: \implies{\sf{36x - 35x } = {20 - 16}}}$

$\quad {: \implies{\sf{x = 4}}}$

$\dag{\underline{\boxed{\sf{x = 4}}}}$

$\begin{gathered}\end{gathered}$

$\dag \: {\underline{\pmb{\frak{\color{purple}{Their \: present \: ages }}}}}$

• ➤ 7x = 7×4 = 28 years
• ➤ 9x = 9×4 = 36 years

$\begin{gathered}\end{gathered}$

${\therefore} \: \begin{gathered}{\textsf{\textbf{\underline{\underline{\color{red}{The option {\green{b)28, 36} }is the correct answer }}}}}}\end{gathered} \blue\checkmark$