Question

The ratio of father to son's age is 7:3. And product of their ages is 756 then whatwill be the ratio if their ages after 6yrs?

Answer 1

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Information given :

✴ Ratio of father's age to son's age = 7:3

✴ The product of their ages = 756


$\red{Solution : }$

Let the father's age be 7a

Let the son's age be 3a

Product of their ages = 756

$7a \times 3a = 756$

$21 {a }^{2} = 756$

${a}^{2} = 756 \div 21$

${a}^{2} = 36$

$a = \sqrt{36}$

$a = 6$

Therefore , Father's age = 7a = 7×6 = 42years

son's age = 3×6= 18 years


$\orange{ After \: 6 \: years : }$

Father's age = 42+6 =48

son's age = 18+6 = 24

Ratio of their ages = 48:24 = 2:1


Hence, The ratio of ages of Father and son after 6 years is 2:1

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Answer 2

Let the age  of  father be  x  and  age  of  son y

according to question,

ratio of  ages = 7:3

x/y = 7/3

3x = 7y

x = 7y/3 .................i)

Sum of ages = 756

xy = 756

putting  x = 7y/3  

(7y/3) y =  756

7y² = 756 × 3

7y² = 2268

y² = 324

y = 18 years

putting y = 18 in eq i)

x = (7×18)/3 = 7 × 6  = 42

x = 42 years

Hence,

Age of Father = 42 years

Age of  Son  = 18 years

After 6 years,

Age of father = 42 + 6 = 48 years

Age of son     =  18 + 6 = 24 years

Ratio of ages = 48/24 = 2:1