Question

The present ages of A and B are in the ratio 7:5.Ten years later,their ages will be in the ratio 9:7.find their present ages.​

Answer 1

Answer:-

Given:-

Ratio of present ages of A and B = 7 : 5.

Let,

A's present age be 7x years and B's present age be 5x years.

Also given that,

After 10 years , the ratio becomes 9 : 7.

According to above condition;

⟹ 7x + 10 : 5x + 10 = 9 : 7

⟹ 7(7x + 10) = 9(5x + 10)

⟹ 49x + 70 = 45x + 90

⟹ 49x - 45x = 90 - 70

⟹ 4x = 20

⟹ x = 20/4

⟹ x = 5

∴

• A's present age = 7x = 7(5) = 35 years.
• B's present age = 5x = 5(5) = 25 years.

Answer 2

Given:

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

Tofind:

• Their present ages.

Solution:

Consider,

• Present age of A = 7x years
• Present age of B = 5x years

After 10 years,

Age of A = (7x+10) years

Age of B = (5x+10) years

According to the question :-

• 10 years later, there ages will be in the ratio of 9:7.

$\to\sf{(7x+10):(5x+10)=9:7}$

$\to\sf{\dfrac{(7x+10)}{5x+10)}=\dfrac{9}{7}}$

$\to\sf{49x+70=45x+90}$

$\to\sf{49x-45x=90-70}$

$\to\sf{4x=20}$

$\to\sf{x=5}$

★ 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.