Question

Q7 Kapil is three years older than Amit. Six years ago Kapil's age was four times Amit's Age . Find
their present ages.

Answer 1

Answer:

Kapil = 8 years

Amit's age = 5 years

Step-by-step explanation:

Given

• Kapil is three years older than Amit.

• Six years ago , Kapil's age was four times Amit's age.

To Find

• Present ages =?

Solution:

Assuming the present age of Amit to be x.

As question says that Kapil is 3 years older than Amit.

So, Present age of Kapil = x + 3

6 years ago, Age of Kapil was 4 times present age.

Equation Formed :

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

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

Subtracting 4x from both the sides :-

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf x - 9 \blue{- 4x} = 4x - 24 \blue{ - 4x}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf - 3x - 9 = - 24$

Adding 9 to both the sides :-

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \ - 3x - 9 \red{ + 9} = - 24 \red{ + 9}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \ - 3x = - 15$

Dividing both sides by (-3) :-

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \dfrac{ - 3x}{ \green{ - 3}} = \dfrac{ - 15}{ \green{ - 3}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf x = 5$

We earlier assumed that :

Amit age = x = 5years.

Kapil's age = x + 3 = 8 years.

Answer 2

Answer:

Kapil - 8 years

Amit- 5 years

Step-by-step explanation:

let amit's age be - x

Kapil- 3+x

Forming the equation -

(x+3)-6=4(x-6)

x= 5

therefore , Kapil's age- 5+3= 8

Amit's age - 5