Question

Let Kanika's present age be $x$ years. Complete the following table, showing ages of her relatives.

$\begin{array}{ccc}& \text{Situation (described in ordinary language)}& \text{Expression}\\ \left(i\right)& \text{Her brother is 2 years younger}.& ---\\ \left(ii\right)& \text{Her father's age exceeds her age by 35 years}.& ---\\ \left(iii\right)& \text{Mother's age is 3 years less than that of her father}.& ---\\ \left(iv\right)& \text{Her grandfather's age is 8 times of her age}.& ---\end{array}$

Answer 1

(i)

Given, Kanika's present age = $x$ years

To get Kanika's brother's age, $2$ should be subtracted from her age since Kanika's brother is $2$ years younger to her.

$\therefore$Kanika's brother's age $=(x-2)$ years

(ii)

Given, Kanika's present age = $x$ years

Since Kanika's father's age exceeds her age by $35$ years, $35$ should be added to her age to get her father's age.

$\therefore$Kanika's father's age $=$ Kanika's present age $+35$ $=(x+35)$ years

(iii)

Given, Kanika's present age $=x$ years

Her father's age $(=x+35)$ years

Since her mother's age is $3$ years less than his father's age,

Mother's age $=$ Father's age $-3$) $=x+35-3=(x+32)$ years

(iv)

Given, Kanika's present age $=x$ years

Kanika's grandfather's age $=8$ times of Kanika's age

$=8\times x=8x$ years