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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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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[tex]\huge\mathfrak{\bf{\underline{\underline{\blue{Solution \ :}}}}}[/tex]
[tex]\longrightarrow \mathsf{Let \: The \: Present \: Age \: of \: A = \underline{ 7x \: Years}}[/tex]
[tex]\longrightarrow \mathsf{Let \: The \: Present \: Age \: of \: B = \underline{5x \: Years}}[/tex]
[tex] \longrightarrow\mathsf{After \: 10 \: Years \: Their \: Age \: Will \: Be ,}[/tex]
[tex]\longrightarrow \mathsf{A = 7x + 10 \: Years\: and}[/tex]
[tex]\longrightarrow \mathsf{B = 5x + 10 \: Years}[/tex]
[tex]\longrightarrow \mathsf{The \: Ratios \: Of \: Their \: Ages \: After \: 10 \: Years \: is \: 9:7}[/tex]
[tex] \therefore \: \: \: \: \: \: \: \: \: \: \: \: \mathsf{ \frac{7x + 10}{5x + 10} = \frac{9}{7} } \\ [/tex]
[tex] \implies \: \mathsf{49x - 45x = 90 - 70}[/tex]
[tex] \implies \: \mathsf{ \cancel4 ^{1} x = \cancel{20} \: ^{5} } [/tex]
[tex] \implies \: \boxed{ \mathsf{\bold{x = 5}}}[/tex]
[tex] \mathsf{Present \: Ages \: of \: A \: = \: 7 \: × \: 5 \: = \: 35 \: Years}[/tex]
[tex] \mathsf{Present \: Ages \: of \: B= \: 5\: × \: 5 \: =25 \: Years}
[/tex]
[tex]\huge{\dag} \: {\sf{\purple{\mathtt{ \underline{Answer}}}}} \ {\dag}[/tex]
[tex] \implies \boxed{{ \mathsf \blue{Present \: Ages \: of \: (A,B) = (35,25)}}}[/tex]
[tex]\Huge\mathbb{\color{maroon}{✩SOLUTION:-}}[/tex]
[tex]\:[/tex]
[tex]\LARGE\mathbb{\color{goldenrod}{✩GIVEN:-}}[/tex]
[tex]\longrightarrow[/tex] Ratios of a and b = [tex]\mathtt{7:5}[/tex]
[tex]\longrightarrow[/tex] Ratios of ages after 20 yrs = [tex]\mathtt{9:7}[/tex]
[tex]\LARGE\mathbb{\color{goldenrod}{✩TOFIND:-}}[/tex]
[tex]\longrightarrow[/tex][tex]\mathtt{The\: present\:ages\:of \:a\:and\:b}[/tex]
[tex]\LARGE\mathbb{\color{goldenrod}{✩CONSEDERING:-}}[/tex]
[tex]\longrightarrow[/tex][tex]\mathtt\red{Age\:of\:a\:-\:7x}[/tex]
[tex]\longrightarrow[/tex][tex]\mathtt\red{Age\:of\:b\:-\:5x}[/tex]
[tex]\:[/tex]
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 [tex]\mathtt\red{(7x+10)}[/tex] and the age B after 10 yrs will be [tex]\mathtt\red{(5x+10)}[/tex]
But we know that the ratio of ages after 10 yrs is 9:7 , so by putting it together we get equation as :
[tex]\:[/tex]
[tex]✩\implies[/tex] [tex]\Large{\frac{7x+10}{5x+10}}[/tex] = [tex]\Large{\frac{9}{7}}[/tex]
[tex]\:[/tex]
[tex]✩\implies[/tex] [tex]\Large{\frac{7x+10}{5x+10}}[/tex] × 7 = [tex]\Large{\frac{9}{7}}[/tex] × 7
[tex]✩\implies[/tex] [tex]\Large{\frac{49x+70}{5x+10}}[/tex] = 9
[tex]✩\implies[/tex] [tex]\mathtt\green{49x+70=45x+90}[/tex]
[tex]✩\implies[/tex] [tex]\mathtt\green{49x=45x+90-70}[/tex]
[tex]✩\implies[/tex] [tex]\mathtt\green{49x-45x=20}[/tex]
[tex]✩\implies[/tex] [tex]\mathtt\green{4x=20}[/tex]
[tex]✩\implies[/tex] [tex]\mathtt{x={\frac{20}{4}}}[/tex]
[tex]✩\implies[/tex] [tex]\large\mathtt{\green{\underline{x=05}}}[/tex]
[tex]\:[/tex]
Therefore ,
[tex]✩\implies[/tex] A's present age = 7x = 7 × 5 = 35 yrs
[tex]✩\implies[/tex] B's present age = 5x = 5 × 5 = 25 yrs
[tex]\:[/tex]