Question

the present ages of A and B are in the ratio 7 ratio 5 .ten years later their ages will be in the ratio 9 ratio 7 . find their present aged​

Answer 1

CORRECT QUESTION :-

★ The present ages of A and B are in the ratio 7:5. 10 years later their ages will be 9:7 . Find their present ages.

GIVEN :-

• The present ages of A and B are in the ratio 7:5.
• 10 years later their ages will be 9:7.

TO FIND :-

• Their present ages.

SOLUTION :-

Let the ratio constant be "x".

★ Present age of A = 7x.

★ Present age of B = 5x.

Ten years Later,

• Age of A = (7x + 10) years.
• Age of B = (5x + 10) years.

☢ ACCORDING TO QUESTION ☢

→ (7x + 10)/(5x + 10) = 9/7

★ By cross multiplication

→ 7(7x + 10) = 9(5x + 10)

→ 49x + 70 = 45x + 90

→ 49x - 45x = 90 - 70

→ 4x = 20

→ x = 20/4

→ x = 5

★ Present age of A = 7x = 35 years.

★ Present age of B = 5x = 25 years.

Hence the present age of A and B are 35 years and 25 years respectively.

Answer 2

⛄GIVEN⛄

• Ratio of their present ages = 7:5
• 10 years later the ratio will be = 9:7

⛄TO FIND⛄

• Their present ages = ?

⛄SOLUTION⛄

Let, the present age of A's be 7x

and, Present age of B's be 5x

Now,

➨ 10 years later A's age = (7x+10) years

➨ 10 years later B's age = (5x+10) years

$\mathbb{ACCORDING \: TO \: QUESTION}$

$\bold{ ➢ \frac{7x + 10}{5x + 10} = \frac{9}{7} }$

→ now, by cross Multiplication

$\bold{ ➢ 7(7x + 10) =9( 5x + 10) }$

$\bold{ ➢ 49x + 70=45x + 90 }$

→ collect like terms

$\bold{ ➢ 49x - 45x=90 - 70}$

$\bold{ ➢ 4x =20}$

$\bold{ ➢ x = \frac{ \cancel{20}}{ \cancel{4}} = 5}$

Hence, x = 5

So,

Present age of A's will be = 7x = 7×5 = 35 years

Present age of B's will be = 5x = 5×5 = 25 years

VERIFICATION

$\bold{ ➟ \frac{35}{25} = \frac{7}{5} }$

$\bold{ ➟ \frac{ \cancel{35}}{ \cancel{25}} = \frac{7}{5} }$

$\bold{ ➟ \frac{ 7}{ 5} = \frac{7}{5} }$

HENCE, VERIFIED✔️