Question

Vikas is three years older than Deepika. Six years ago, Vikas's age was four times
Deepika's age. Find the ages of Deepika and Vikas.
​

Answer 1

Let deepika age be x years

Vikas age = x + 3

6 years ago:

Deepika age = x - 6

Vikas age = x+3-6 = x-3

As per the question, vikas age is 4 times the deepika age

x - 3 = 4(x-6)

x-3 = 4x - 24

3x = 21

x = 7

Deepika age = 7 yrs

Vikas age = 7+3 = 10

Answer 2

$\Large\sf\orange{Question:}$

Vikas is three years older than Deepika. Six years ago, Vikas's age was four times Deepika's age. Find the ages of Deepika and Vikas.

$\Large\sf\orange{Given:}$

Vikas is three years older than Deepika.

Six years ago, Vikas's age was four times Deepika's age.

$\Large\sf\orange{To\:find:}$

Ages of Deepika and Vikas .

$\Large\sf\orange{Solution:}$

$\tt\green{Let\: us \:consider,}$

$\tt{Age\: of \:Deepika\: as\: 'x'\: years.}$

$\tt{Age \:of\: Vikas \:age \:as \:(x + 3) \:as \:mentioned.}$

$\tt\green{Now,\:Let\: us \:consider,}$

$\tt{Age \:of \:Deepika\: 6 \:years \:ago = x - 6}$

$\tt{Age \:of \:Vikas\: 6 \:years \:ago = x + 3 - 6 = x -3}$

$\tt{It \:is\: given\: that\: age\: of \:Vikas\: is\: 4 \:times \:that \:of \:Deepika's \:age }$

$\tt{ Therefore ,\:Age \:of\: Vikas = 4 \times (x - 6)}$

$\sf\pink{According\:to\: the \:statement :}$

$\sf\implies(x-3) = 4(x-6)$

$\sf\blue{Simplify\:the\:expression:}$

$\sf\implies(x-3) = (4x-24)$

$\sf\implies(4x-x) = (24-3)$

$\sf\implies(3x) = (21)$

$\sf\implies x = \dfrac{21}{3}$

$\sf\implies x = 7$

$\tt\red{Deepika's\:Age=7\:years}$

$\tt\red{Vikas's\:Age=x+3 = 7+3 =10\:years}$