Question

The ratio of the ages of the husband and the wife five years ago was 11:9 where as at the same time the ratio of the ages of the husband and his son was 5:1 .Five years hence the ratio of the ages of the husband and the wife became 13:11 . What is the sum of the present ages of all the three persons of the family ?​

Answer 1

Answer:

Step-by-step explanation:

Given :

The ratio of a husband & his wife 5 years ago was = 11 : 9

The ratio of a husband & his son 5 years ago was = 5 : 1

The ratio of a husband & his wife 5 years after was = 13 : 11

To Find :

The sum of the present ages of all 3 persons in the family.

Solution :

Let the present age of husband be x,

Let the present age of wifw be y,

Let the present age of son be z,

Then,

The age of husband 5 years ago = x - 5

The age of wife 5 years ago = y - 5

Then, $\frac{x-5}{y-5} = \frac{11}{9}$

9(x - 5) = 11(y - 5)

9x - 45 = 11y - 55

⇒ 9x - 11y = -10 ...(i)

_

The age of husband 5 years after will be x + 5

The age of wife 5 years after will be y + 5

Then, $\frac{x+5}{y+5} = \frac{13}{11}$

11(x + 5) = 13(y + 5)

11x + 55 = 13y + 65

⇒ 11x - 13y = 10 ...(ii)

By solving (i) & (ii),

By subtracting 9×(ii) , from 11×(i),

We get,

11(9x - 11y) - 9(11x - 13y) = 11(-10) - 9(10)

99x - 121y - 99x + 117y = -110 - 90

-4y = -200 ⇒ y = 50

By substituting value of y in (i),

We get,

9x - 11(50) = -10

9x - 550 = -10

9x = 540 ⇒ x = 60

_

The age of son 5 years ago = z - 5,.

then,

$\frac{x - 5}{z - 5} = \frac{5}{1}$

$\frac{60 - 5}{z - 5} = 5$

55 = 5(z - 5)

55 = 5z - 25

30 = 5z ⇒ z = 6

∴ The sum of the present ages of the 3 persons of the family = (x + y + z) = 60 + 50 + 6 = 116

Answer 2

Answer:

Step-by-step explanation:

Five years ago,

H:W= 11:9

and H:S = 5:1

Hence, H:W:S =55:45:11

55k+10. =13

_________

45k+10. =11

Five years hence,

k=1

Required value =55+45+11+15=126years