Question

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

Answer 1

Answer:

The ratio of their ages after 10 years is 9:7. age of B= 5×5=25 years.

Let we take A name Lena and B name Hena.

Let the rational between ages of Leena and Heena be x

The ages of Leena and Heena are in the ratio 7:5.

Thus there ages are, Leena 7x and Heena 5x

Ten years hence, the ratio of their ages will be 9:7.

10 year hence their ages will be

Leena’s age 7x + 10

Heena’s age 5x + 10

The ratio of their ages

7x + 10 / 5x + 10 = 9 / 7

Cross multiplication

9 ( 5x + 10 ) = 7 ( 7x + 10 )

45x + 90 = 49x + 70

45x - 49x = 70 - 90

—5x = -20

5x = 20

x = 20/5

x = 4

The rational is 4

Their respective ages

Leena’s age 7x = 7 × 4 = 28 years

Heena’s age 5x = 5 × 4 = 20 years

Answer 2

Answer:

Let the present age of A= 7x years

The present age of B= 5x years

After 10 years, their ages will be 

A=7x+10 years and

B=5x+10 years

The ratio of their ages after 10 years is 9:7.

∴5x+107x+10=79

⇒49x+70=45x+90

⇒49x−45x=90−70

⇒4x=20

⇒x=5

∴ Present age of A= 7×5=35 years and present 

age of B= 5×5=25 years.