the present age of Aand B are in the ratio 7:5 and 10 years later their age will be in the ratio 9:7 find the present age
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the present age of Aand B are in the ratio 7:5 and 10 years later their age will be in the ratio 9:7 find the present age
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• Given
• To find
• Solution
According to the question,
Let the age of A and b be 7x and 5x
:[tex]\implies \sf{ \dfrac{7x + 10}{5x + 10} = \dfrac{9}{7}}[/tex]
: [tex]\implies \sf{7(7x + 10) = 9(5x + 10)}[/tex]
: [tex]\implies \sf{49x + 70 = 45x + 90}[/tex]
: [tex]\implies \sf{49x - 45x = 90 - 70}[/tex]
: [tex]\implies \sf{4x = 20}[/tex]
: [tex]\implies \sf{x = \dfrac{20}{4}}[/tex]
: [tex]\green{\bigstar}[/tex] [tex]\underline{\boxed{ \sf \blue{x = 5}}}[/tex]
[tex]\red{\bigstar}[/tex] [tex]\underline{\boxed{ \sf \blue{Present ~age ~of ~A~ = 7x ~= 7 × 5 = 35 ~years.}}}[/tex]
[tex]\red{\bigstar}[/tex] [tex]\underline{\boxed{ \sf \blue{Present ~age ~of ~B ~= 5x~ = 5 × 5 = 25~ years}}}[/tex]