Question

10. Ankia's mother's age is two and half times Ankita's age and four times her brother's age. Their total age is 66 years. What will be Ankita's brother's age fa 2 years? (1) 10 years (2) 12 years (3) 14 years (4) 16 years. 02​

Answer 1

Correct Question

Ankita's mother's age is two and half times Ankita's age and four times her brother's age. Their total age is 66 years. What will be Ankita's brother's age after 2 years?

(1) 10 years

(2) 12 years

(3) 14 years

(4) 16 years

Answer

Given :

Sum of all ages : 66 years

Mother's age is two and half times Ankita's age.

Her brother's age is 4 times smaller than her mother.

To find :

The age of Ankita's brother, after 2 years.

Solution :

Let the age of Ankita be x years.

Let the age of her mother be 2½x years.

Let the age of her brother be 2½x/4 years.

According to the question,

Age of Ankita :

$\sf \dashrightarrow x + 2 \dfrac{1}{2}x + \dfrac{2 \dfrac{1}{2}x}{4} = 66$

$\sf \dashrightarrow x + \dfrac{5}{2}x + \dfrac{\dfrac{5}{2}x}{4} = 66$

$\sf \dashrightarrow x + \dfrac{5x}{2} + \dfrac{5x}{2(4)} = 66$

$\sf \dashrightarrow x + \dfrac{5x}{2} + \dfrac{5x}{8} = 66$

$\sf \dashrightarrow \dfrac{8x + 20x + 5x}{8} = 66$

$\sf \dashrightarrow \dfrac{33x}{8} = 66$

$\sf \dashrightarrow 33x = 66 \times 8$

$\sf \dashrightarrow 33x = 528$

$\sf \dashrightarrow x = \dfrac{528}{33}$

$\sf \dashrightarrow x = 16$

Age of Ankita's mother :

$\sf \dashrightarrow 1 \dfrac{1}{2}x = \dfrac{5}{2}x$

$\sf \dashrightarrow \dfrac{5(16)}{2} = \dfrac{80}{2}$

$\sf \dashrightarrow 40 \: years$

Age of Ankita's brother :

$\sf \dashrightarrow \dfrac{1 \dfrac{1}{2}x}{4} = \dfrac{\dfrac{5}{2}x}{4}$

$\sf \dashrightarrow \dfrac{\dfrac{5(16)}{2}}{4} = \dfrac{\dfrac{80}{2}}{4}$

$\sf \dashrightarrow \dfrac{80}{2(4)} = \dfrac{80}{8}$

$\sf \dashrightarrow 10 \: years$

Now, we can find the age of Ankita's brother, 2 years later.

Age of brother (2 years later) :

$\sf \dashrightarrow 10 + 2$

$\sf \dashrightarrow 12 \: years$

Hence, the age of her brother, 2 years later is 12 years. Thus, Option (2) is the correct option.

Answer 2

Answer:

12 years

Step-by-step explanation: