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Q 53 The age of Ranbir is the square the age of his son. If the sum of ages of Ranbir and five times the age of his son is 66 years, then their ages are:
5 years, 25 years
9 years, 81 years
Ops: A.
B.
C.
D.
6 years, 36 years
7 years, 49 years​

Answer 1

Answer:

I don't know the answer

Answer 2

Answer:

6 years, 36 years

Step-by-step explanation:

Let the age of Ranbir = x

Age of his son = y

According to first condition of the question:-

The age of Ranbir is the square of the age of the son.

i.e.    $x = y^{2}$   -------------------- 1

According to the second condition:-

The sum of ages of Ranbir and five times the age of his son is 66.

i.e.  x + 5y = 66     -------------------- 2

Solving equation 2

x + 5y = 66

x = 66 - 5y

Put the value of x in equation 1

$y^{2} = 66 - 5y \\y^{2} + 5y -66 = 0$

Solving by the factorial method

$y^{2} + ( 11y - 6y) - 66 = 0 \\y^{2} + 11y - 6y - 66 = 0 \\y(y+11) - 6(y + 11) = 0 \\(y + 11) (y - 6) = 0$

If y + 11 = 0

Then y = -11 (impossible because age can not be in '-ive' sign)

If y - 6 = 0

Then y = 6

Hence the age of the son is 6

Now, from equation 2

x + 5y = 66

Put y = 6, We get-

x + 5×6 = 66

x + 30 = 66

x = 66 - 30

x = 36

Hence the age of Father is 36

Age of father = 36

Age of son = 6