Question

If the present ages of A and B are in the ratio of 9 : 4 and seven years hence, the ratio of their ages will be 5 : 3 , then find their present ages..

Answer 1

$\underline{\textbf{Hey Mate Here is Your answer }}$

$\underline{\textbf{Given That}}$

The Present Ages Of A and B are in the ratio 9:4 and seven years hence,the ratio of their ages will be 5:3,

Now We Need to find their present ages.

So now let's Move For Solution

$\underline{\textbf{Solution}}$

So In Question It's Given that

$\mathbf{ A\::\:B \: = \: 9 \::\:4}$. ( Present Age )

So Now

$\textbf{ Let X Be the Constant Of Ratio }$

Therefore

$\textbf{Present Age Of A = 9x }$

$\textbf{Present Age Of B = 4x }$

$\underline{\textbf{Age Of A \& B After 7 Years }}$

$\textbf{Age Of A After 7 Years = 9x + 7 }$

$\textbf{Age Of B After 7 Years = 4x + 7 }$

So Now According To Question It's Said That

$\textbf{After 7 Years Ratio Of Their Ages Would Be Equal To 5 : 3 }$

Therefore We Have ​

$\large{\mathbf{\frac{9x\: +\:7}{4x \: + \:7 } \: = \: \frac{5}{3}}}$

Now Cross Multiplying LHS And RHS We Have ​

$\mathbf{ 3( \: 9x \: + \: 7 \:) \: = \: 5 ( \: 4x \:+ \:7\: ) }$

$\mathbf{ 27x \: + \: 21 \: = \:20x \:+ 35\: }$

Now Taking Variable terms to LHS And Constant terms To RHS We Have ​

$\large{\mathbf{ 7x \: = \: 14 }}$

Now Taking 7 To LHS We Have

$\mathbf{ X\: = \: 14/7 \: = \:2 }$

$\mathbf{ \therefore\; We\: Have \: Value \: Of\: \boxed{X\: = \:2 }}$

$\underline{\textbf{Now Putting Obtained Value Of X In the Present Ages We Have }}$

$\underline{\mathbf{Present\: Age\: Of \: A \: = 9x \:\longrightarrow \: 9 \times 2 \:=\: 18 \:Years}}$

$\underline{\mathbf{Present\: Age\: Of \: B \: = 4x \:\longrightarrow \: 4 \times 2 \:=\: 8 \:Years}}$

$\underline{\textbf{Hence The Required Answer Is }}$

$\boxed{\mathbf{Age\: of\: A\: = \:18 years \:And \: Age \: Of \: B\: = \: 8\: Years }}$

$\large{\blue{Thanks..}}$

$\underline{\large{\star\:\: BrainlyKing5 \:\: \star}}$

Answer 2

Answer:

A = 18 yrs

B = 8 yrs

Step-by-step explanation:

$\text{Present ratio of ages of A and B = 9:4}\\\\\text{Let the present age of A be 9x and of B be 4x}\\\\\text{After 7 years, A's age = 9x+7 and B's age = 4x+7}\\\\\text{But, given ratio of ages of A and B after 7 years = 5:3}\\\\\text{Thus, According to the question,}\\\\\dfrac{9x+7}{4x+7} = \dfrac{5}{3}\\\\\\\implies 3(9x+7) = 5(4x+7)\\\\\implies 27x + 21 = 20x + 35\\\\\implies 27x-20x = 35-21\\\\\implies 7x = 14\\\\\implies x = \dfrac{14}{7}\\\\\\\implies x = 2$

$\therefore \text{Present age of A = 9x = 9(2) = 18 years}\\\\\text{And, present age of B = 4x = 4(2) = 8 years}$

Hope it helps.