Question

(ii) A man is 3(1/2) times as old as his son. If the sum of the squares of their ages is 1325, find the ages of the father and the son.​

Answer 1

Step-by-step explanation:

son age=x

A man age=3(1/2)x

according to question

(x)^2+(3(1/2))^2=1325

x^2+(7/2)^2=1325

x^2+49/4=1325

x^2=1325X4/49

x^2=5408/49

(x)^2=(73.53/7)^2

x=73.53

age of son=73.53

father age=3(1/2)X73.53=514.71/2=257.355

Answer 2

Given:

A man is 3(1/2) times as old as his son. If the sum of the squares of their ages is 1325.

To find:

The ages of the father and the son.

Solution:

Let the age of the son be x years.

So,

the age of the father

$= (3 \frac{1}{2} \times x) \: years$

$= \frac{7}{2} x \: years$

Now,

according to the question, we have,

the sum of the squares of ages of father and son is 1325.

So,

${x}^{2} + { (\frac{7x}{2} )}^{2} = 1325$

${x}^{2} + \frac{ {49x}^{2} }{4} = 1325$

On taking 4 as LCM, we have,

$\frac{53 {x}^{2} }{4} = 1325$

${x}^{2} = \frac{1325 \times 4}{53}$

${x}^{2} = 25 \times 4$

${x}^{2} = 100$

On taking square root on both sides, we get

$x = 10 \: years$

So, the age of the father

$= \frac{7}{2} \times 10$

$= 35 \: years$

Hence, the present age of father and son is 35 years and 10 years respectively.