Question

My sister's age is 3 less than my age.

Six years ago I was double of my sisters age.

What will be the age of me and my sister?

Answer 1

Required Answer :

• My present age = 12 years
• The present age of my sister = 9 years

Given :

• My sister's age is 3 less than my age.
• Six years ago, I was double of my sister's age

To find :

• Present age of me and my sister

Solution :

Let,

• My present age = x years
• My sister's present age = x - 3 years

6 years ago, the ages were :

⇒ My age = x - 6 years

⇒ My sister's age = x - 3 - 6

⇒ My sister's age = x - 9 years

According to the question,

⇒ My age = 2(My sister's age)

⇒ (x - 6) = 2(x - 9)

⇒ x - 6 = 2x - 18

⇒ x - 2x = - 18 + 6

⇒ - x = - 12

⇒ x = 12

⇒ The value of x = 12

Substituting the value of x :

My present age :

⇒ My present age = x

⇒ My present age = 12 years

My sister's present age :

⇒ My sister's present age = x - 3

⇒ My sister's present age = 12 - 3

⇒ My sister's present age = 9 years

Answer 2

$\small{{ \boxed{\boxed{\begin{array}{cc} \bf \: \leadsto \: given \\ \\ \rm \to \: My \: sister's \: age \: is \: 3 \: less \: than \: my \: age \: \\ \\ \rm \to \: Six \: years \: ago \: I \: was \: double \: of \: my \: sister's \: age \: \\ \\ \underline{ \leadsto \: \sf \: we \: have \: to \: find : } \\ \\ \rm \to \: Present \: age \: of \: me \: and \: my \: sister \: \end{array}}}}}$

$\small{{ \boxed{\boxed{\begin{array}{cc} \rm \: Let \: us \: assume \: that,\: \\ \\ \pink{\rm \: \to \: My \: present \: age \: is = x \: years }\\ \\ \pink{\rm \: \to \: My \: sister's \: present \: age \: is \: = (x - 3) \: years }\\ \\ \sf \: and \: 6 \: years \: ago\: our \: ages \: were \: \\ \\ \rm \to \: My \: age = x - 6 years \\ \\ \rm \to \: My \: sister's \: age \: = (x - 3) - 6 =( x - 9) \: years \\ \\ \\ \bf \: according \: to \: the \: question, \\ \\ \rm \: (x - 6) = 2(x - 9) \\ \\ \rm \to \: x - 6 = 2x - 18 \\ \\ \rm \to \: x - 2x = - 18 + 6 \\ \\ \rm \to \: \cancel{- }x = \cancel{- }12 \\ \\ \therefore \: \rm \: x = 12\end{array}}}}}$

Finally,

$\small{\pink{ \boxed{\boxed{\begin{array}{cc} \rm \: \to \: My \: present \: age \: is = 12 \: years \\ \\ \rm \: \to \: My \: sister's \: present \: age \: is \: = (12- 3) = 9\: years \end{array}}}} }$