Question

A's age is square of his daughter's age. If the
sum of their ages is 72, then A's age is​

Answer 1

$\large\red{\underline{\underline{\bf{\blue{Given}}}}}$

• A's age is square of his daughter's age.

• Sum of their ages = 72

$\large\red{\underline{\underline{\bf{\blue{To\:Find}}}}}$

• A's age

$\large\red{\underline{\underline{\bf{\blue{Solution}}}}}$

Let daughter's age be "x" years and A 's age be "y" years

Then,

• According to 1st condition :-

A' s age is => y = x^2. ---(1)

• According to 2nd condition :-

= > B + A = 72

=> x + y = 72 ---(2)

Put the value of 1st eq in 2nd eq, we get,

$= > x + {x}^{2} = 72 \\ \\ = > {x}^{2} + x - 72 = 0 \\ \\ = > {x}^{2} + 9x - 8x - 72 = 0 \\ \\ = > x(x + 9) - 8(x + 9) = 0 \\ \\ = > (x - 8)(x + 9) = 0 \\ \\ = > x = 8 \: \: or \: x = - 9$

Hence,

Age can't be negative.

So, x = 8 years

Then,

• A's age = y = x^2 = 8^2 = 64 years

• B ' s age = x = 8 years

Answer 2

✬ A's age = 64 Years ✬

Step-by-step explanation:

Given:

• A's age is square of his daughter's age.
• Sum of A's and daughter's age is 72.

To Find:

• What is A's age ?

Solution: Let the A's age be x years and daughter's age be y years.

➼ A's age = Square of daughter's age

➼ x = y²........(1)

A/q

➟Sum of A's age and daughter's age is 72 .

$\implies{\rm }$ A's age + Daughter's age = 72

$\implies{\rm }$ x + y = 72

$\implies{\rm }$ y² + y = 72 { From equation 1 }

$\implies{\rm }$ y² + y – 72 = 0

$\implies{\rm }$ y² + 9y – 8y – 72 = 0 { By middle term splitting }

$\implies{\rm }$ y ( y + 9 ) – 8 ( y + 9 ) = 0

$\implies{\rm }$ ( y – 8 ) ( y + 9 )

$\implies{\rm }$ y – 8 = 0 or y + 9 = 0

$\implies{\rm }$ y = 8 or y = – 9

Since, age can't be in negative therefore y = 8 years.

∴ A's age = x = (y)² = 8² = 64 Years.

Hence, the age of A is 64 years.

______________________

★ Verification ★

➱ A's age + Daughter's age = 72 years

➱ 64 + 8 = 72

➱ 72 = 72

[ Thus, Verified ]