Question

the age of two frnds is in the ratio 5:6. after how many years will the ages be in the ratio 7:8​

Answer 1

GIVEN :–

• The age of two friends is in the ratio 5:6.

TO FIND :–

• After how many years will the ages be in the ratio 7:8 ?

SOLUTION :–

• The age of two friends is in the ratio 5:6. So we can consider their ages as 5x and 6x .

• Now new age ratio –

$\\ \implies \bf \dfrac{5x + a}{6x +a} = \dfrac{7}{8}$

$\\ \implies \bf (5x + a)(8) = (6x +a)(7)$

$\\ \implies \bf 40x + 8a = 42x + 7a$

$\\ \implies \bf 8a - 7a = 42x - 40x$

$\\\large\implies{ \boxed{ \bf a = 2x}}$

• Hence , After two time of present age will make the age ratio as 7:8.

VERIFICATION :–

$\\ \implies \bf Present\:\:age\:\:is = \dfrac{5x}{6x}=\dfrac{5}{6}$

• After '2x' year –

$\\ \implies \bf Age\:\:ratio = \dfrac{5x+2x}{6x+2x}$

$\\ \implies \bf Age\:\:ratio = \dfrac{7x}{8x}$

$\\ \implies \bf Age\:\:ratio = \dfrac{7}{8}$

$\\\large\implies{ \boxed{ \bf Hence\:\:Verified\:\checkmark}}$