19. The ages of Leena and Heena are in the ratio 7:5. Ten years later,

1.	19. The ages of Leena and Heena are in the ratio 7:5. Ten years later, the ratio of their ages will be 9:7.Find their present ages.
Answer» Let Leena's age be x and Heena's age be y. x/y = 7/5 5x = 7y 5x - 7y = 0 . . . . . (1) (x + 10)/(y + 10) = 9/7 7x + 70 = 9y + 90 7x - 9y = 20 . . . . . (2) (1) × 7 35x - 49y = 0 . . . . . (3) (2) × 5 35x - 45y = 100 . . . . . (4) (3) - (4) -4y = -100 y = 25 5x = 7 × 25 x = 35 Leena is 35 years and Heena is 25 years

19. The ages of Leena and Heena are in the ratio 7:5. Ten years later, the ratio of their ages will be 9:7.Find their present ages.

Answer»

Let Leena's age be x and Heena's age be y.

x/y = 7/5

5x = 7y

5x - 7y = 0 . . . . . (1)

(x + 10)/(y + 10) = 9/7

7x + 70 = 9y + 90

7x - 9y = 20 . . . . . (2)

(1) × 7

35x - 49y = 0 . . . . . (3)

(2) × 5

35x - 45y = 100 . . . . . (4)

(3) - (4)

-4y = -100

y = 25

5x = 7 × 25

x = 35

Leena is 35 years and Heena is 25 years