Question

x.
The present ratio of ages of A & B is 6 : 7. After 5
years this ratio will be changed into 7: 8. Find the
present age of A & B.​

Answer 1

$\sf{\underline{\boxed{\large{\blue{\mathsf{Solution}}}}}}$

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• Present age of A and B = 6 : 7
• After 5 years age of A and B = 7 : 8

_______________________

$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

• Present age of A and B = ??

______________________

$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

Let present age be 6x and 7x

⠀⠀⠀⠀⠀

• After 5 years ratio will be

⠀⠀⠀⠀⠀⠀⠀

:$\sf\implies\: {\bold{\dfrac{6x+5}{7x+5}}}$

⠀⠀

• ATQ:-

:$\sf\implies\: {\bold{\dfrac{6x+5}{7x+5} = \dfrac{7}{8}}}$

⠀⠀⠀⠀

:$\sf\implies\: {\bold{ 8( 6x + 5 ) = 7 ( 7x + 5)}}$

⠀⠀⠀⠀

:$\sf\implies\: {\bold{ 48x + 40 = 49x + 35}}$

⠀⠀⠀⠀

:$\sf\implies\: {\bold{ 49x - 48x = 40 - 35}}$

⠀⠀⠀⠀

:$\sf\implies\: {\bold{ x = 5}}$

⠀⠀⠀⠀

• Putting value of x in their ratio of age

⠀⠀⠀⠀

A's age = 6x = 6 x 5 = 30 years

B's age = 7x = 7 x 5 = 35 years

______________________

$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

• Present age of A and B is 30 years and 35 years .