Question

Q- The present ages of A and B are in the ratio 7:5 , 10 years later their ages will be in ratio 9:7 . Find their present ages.

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Answer 1

$\huge\mathfrak{\bf{\underline{\underline{\blue{Solution \ :}}}}}$

$\longrightarrow \mathsf{Let \: The \: Present \: Age \: of \: A = \underline{ 7x \: Years}}$

$\longrightarrow \mathsf{Let \: The \: Present \: Age \: of \: B = \underline{5x \: Years}}$

$\longrightarrow\mathsf{After \: 10 \: Years \: Their \: Age \: Will \: Be ,}$

$\longrightarrow \mathsf{A = 7x + 10 \: Years\: and}$

$\longrightarrow \mathsf{B = 5x + 10 \: Years}$

$\longrightarrow \mathsf{The \: Ratios \: Of \: Their \: Ages \: After \: 10 \: Years \: is \: 9:7}$

$\therefore \: \: \: \: \: \: \: \: \: \: \: \: \mathsf{ \frac{7x + 10}{5x + 10} = \frac{9}{7} }$

$\implies \: \mathsf{49x - 45x = 90 - 70}$

$\implies \: \mathsf{ \cancel4 ^{1} x = \cancel{20} \: ^{5} }$

$\implies \: \boxed{ \mathsf{\bold{x = 5}}}$

$\mathsf{Present \: Ages \: of \: A \: = \: 7 \: × \: 5 \: = \: 35 \: Years}$

$\mathsf{Present \: Ages \: of \: B= \: 5\: × \: 5 \: =25 \: Years}</p><p>$

$\huge{\dag} \: {\sf{\purple{\mathtt{ \underline{Answer}}}}} \ {\dag}$

$\implies \boxed{{ \mathsf \blue{Present \: Ages \: of \: (A,B) = (35,25)}}}$

Answer 2

$\Huge\mathbb{\color{maroon}{✩SOLUTION:-}}$

$\:$

$\LARGE\mathbb{\color{goldenrod}{✩GIVEN:-}}$

$\longrightarrow$ Ratios of a and b = $\mathtt{7:5}$

$\longrightarrow$ Ratios of ages after 20 yrs = $\mathtt{9:7}$

$\LARGE\mathbb{\color{goldenrod}{✩TOFIND:-}}$

$\longrightarrow$$\mathtt{The\: present\:ages\:of \:a\:and\:b}$

$\LARGE\mathbb{\color{goldenrod}{✩CONSEDERING:-}}$

$\longrightarrow$$\mathtt\red{Age\:of\:a\:-\:7x}$

$\longrightarrow$$\mathtt\red{Age\:of\:b\:-\:5x}$

$\:$

Now , according to question , it is said that after 10 yrs the ratios of ages will be 9:7 .

so , the age of a after 10 yrs will be $\mathtt\red{(7x+10)}$ and the age B after 10 yrs will be $\mathtt\red{(5x+10)}$

But we know that the ratio of ages after 10 yrs is 9:7 , so by putting it together we get equation as :

$\:$

$✩\implies$ $\Large{\frac{7x+10}{5x+10}}$ = $\Large{\frac{9}{7}}$

$\:$

$✩\implies$ $\Large{\frac{7x+10}{5x+10}}$ × 7 = $\Large{\frac{9}{7}}$ × 7

$✩\implies$ $\Large{\frac{49x+70}{5x+10}}$ = 9

$✩\implies$ $\mathtt\green{49x+70=45x+90}$

$✩\implies$ $\mathtt\green{49x=45x+90-70}$

$✩\implies$ $\mathtt\green{49x-45x=20}$

$✩\implies$ $\mathtt\green{4x=20}$

$✩\implies$ $\mathtt{x={\frac{20}{4}}}$

$✩\implies$ $\large\mathtt{\green{\underline{x=05}}}$

$\:$

Therefore ,

$✩\implies$ A's present age = 7x = 7 × 5 = 35 yrs

$✩\implies$ B's present age = 5x = 5 × 5 = 25 yrs

$\:$