Question

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

Answer 1

Answer:

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 the Leena’s age is 28 years and Heena’s age is 20 years

Let the present ages of Leena and Heena be L and H.

L:H = 7:5 …(1), at present

(L+10):(H+10)::9:7 …(2), 10 years from the present

From (1) 7H = 5L …(1a) L = 1.4H

from (2), 7(L+10)=9(H+10), or

7L + 70 = 9H+ 90, or

7L- 9H = 20 …(2a)

7*1.4H - 9H = 20, or

9.8H - 9H = 20, or

0.8H = 20, or

H = 20/0.8 = 25 and L = 1.4*25 = 35

Check: In ten years L = 35+10 = 45 and H = 25+10 = 35 and 45:35 as same as 9:7. Correct.

So the present ages of Leena and Heena are 35 and 25 years, respectively.