Question

Ages of a and b are in the ratio 9:4 seven years later the ratio of their ages be 5:3 ,find their present ages. Let their ages be 9x years and 4x years

Answer 1

Answer

let their ages be 9x and 4x

after seven years

• age of a = 9x + 7
• age of b = 4x + 7

and according to the question,

(seven years later the ratio of their ages be 5:3)

$\bold{: \implies \: \frac{9x + 7}{4x + 7} = \frac{5}{3} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies3(9x + 7) = 5(4x + 7) } \\ \\ \bold{: \implies \: 27x + 21 = 20x + 35 } \\ \\ \bold{: \implies \: 27x - 20x = 35 - 21} \\ \\ \bold{: \implies \: 7x = 14} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{ : \implies \: x = \cancel \frac{14}{7} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies \: \boxed{ \bold{x = 2 }}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

so, x = 2 is common multiple of their ages.

➪ present age of a = 9 × 2 = 18 years

and present age of b = 4 × 2 = 8 years

hence, age of a is 18 years and age of b is 8 years