Question

Ram's age is square of his daughter's age. If the
sum of their ages is 72, then ram's age is...
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Answer 1

Given:

• Ram's age is square of his daughter's age.
• Sum of their age = 72

To Find:

• Ram's age

Solution:

Let daughter's age be "x" years and Ram's age be "y" years.

First Condition:

• Ram's age = y = x² --(1)

Second Condition:

• x + y = 72 --(2)

Putting the values in 1st and 2nd equation,

→ x + x² = 72

→ x² + x - 72 = 0

→ x² + 9x - 8x - 72 = 0

→ x(x + 9) - 8(x + 9) = 0

→ (x - 8) (x + 9) = 0

→ x = 8 and x = -9

Hence,

• Age can't be negative.
• So, x = 8 years

Then,

• Ram's age = y = x² = 8² = 64 years.
• Daughter's age = x = 8 years

Verification:

→ Ram's age + Daughter's age = 72 years

→ 64 + 8 = 72

→ 72 = 72

Hence Verified!

Answer 2

Given :

• Ram's age is square of his daughter's age.
• Sum of their ages is 72 .

To Find :

• Age of Ram .

Solution :

$\longmapsto\tt{Let\:Daughter's\:age\:be=x}$

As Given that Ram's age is square of his daughter's age. So ,

$\longmapsto\tt{Age\:of\:Ram={x}^{2}}$

A.T.Q :

$\longmapsto\tt{x+{x}^{2}=72}$

$\longmapsto\tt{{x}^{2}+x-72=0}$

$\longmapsto\tt{{x}^{2}+9x-8x-72=0}$

$\longmapsto\tt{x(x+9)-8(x+9)=0}$

$\longmapsto\tt{(x-8)\:\:(x+9)=0}$

• x = 8
• x = -9

Age cannot be negative . So , The value of x is 8 .

Therefore :

$\longmapsto\tt{Age\:of\:Ram={8}^{2}}$

$\longmapsto\tt\bf{64\:yrs}$

$\longmapsto\tt{Age\:of\:Daughter=x}$

$\longmapsto\tt\bf{8\:yrs}$

_______________________

VERIFICATION :

$\longmapsto\tt{{x}^{2}+x=72}$

$\longmapsto\tt{{8}^{2}+8=72}$

$\longmapsto\tt{64+8=72}$

$\longmapsto\tt\bf{72=72}$

HENCE VERIFIED