Question

Ram is 3 years older than Rohan. Six years ago, Ram’s age was four times Rohan’s age. Find the present age of Rohan.

Answer 1

GIVEN:

• Ram is 3 years older than Rohan.
• Six years ago, Ram’s age was four times Rohan’s age

TO FIND:

• What are their present ages ?

SOLUTION:

Let the present age of Ram be 'x' years and that of the age of Rohan be 'y' years

CONDITION:- 1)

Ram is 3 years older than Rohan.

According to question:-

$\bf{\longrightarrow x = y +3....1) }$

CONDITION:- 2)

Six years ago, Ram’s age was four times Rohan’s age

• Ram's age = (x–6) years
• Rohan's age = (y–6) years

According to question:-

$\rm{\longrightarrow (x-6) = 4(y-6) }$

$\rm{\longrightarrow x -6 = 4y-24 }$

$\rm{\longrightarrow x-4y = -24 +6}$

$\bf{\longrightarrow x -4y = -18...2) }$

Put the value of 'x' from equation 1) in equation 2)

$\rm{\longrightarrow y+3-4y = -18 }$

$\rm{\longrightarrow -3y = -18-3 }$

$\rm{\longrightarrow -3y = -21 }$

$\rm{\longrightarrow y = \cancel\dfrac{-21}{-3}}$

$\bf{\longrightarrow y = 7}$

Put the value of 'y' in equation 1)

$\rm{\longrightarrow x = 7 +3 }$

$\bf{\longrightarrow x = 10 }$

• Ram's age = x = 10 years
• Rohan's age = y = 7 years

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Answer 2

GIVEN :-

• Ram is 3 years older than Rohan.

• Six years ago, Ram’s age was four times Rohan’s age

TO FIND :-

✳ The present age of Rohan.

SOLUTION :-

Taking,

• Ram's present age be x years .

• Rohan's present age be y years.

Situation 1.

⭐ Ram is 3 years older than Rohan.

↗ x = y + 3.........(1)

Situation 2.

⭐ Six years ago, Ram’s age was four times Rohan’s age

• Ram's age = (x–6) years.

• Rohan's age = (y–6) years.

According to the question,

⭐ (x−6) = 4 (y−6)

⟶ x − 6 = 4y − 24

⟶ x − 4y = − 24 + 6

⟶ x − 4y = −18.....(2)

Putting From 1.in 2 ,

⟶ (y + 3) − 4y = − 18

⟶ − 3y + 3 = − 18

⟶ − 3y = − 18 − 3

⟶ −3y = −21

⟶ y= −21/-3

⟶ y = 21/3

⟶ y = 7

Putting y in 1 ,

▶ x = y + 3

▶ x = 7 + 3

▶ x = 10

➡ Ram is 10 years old & Rohan is 7 year old.

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