Question

Ramu is twice old as somu five years ago his age was three times somu,s age .find their present age

Answer 1

$\sf Let \: the \: present\: age\: Somu\; be\: x \: and \: present\: age \: of \: Ramu \: be \: 2x .$

$\sf Five \: years \: ago\: ,$

$\sf Age\: of \:Somu = x-5\\\sf Age\:of \:Ramu = 2x-5$

$\sf \Longrightarrow 2x-5=3(x-5)\\\\\sf \Longrightarrow 2x-5=3x-15\\\\\sf \Longrightarrow 3x-2x = -5+15\\\\\sf \Longrightarrow x = 10$

$\sf Present \: age \: of \: Somu = 10\: years\\\\\sf Present \: age \: of \: Ramu = 20 \: years$

HOPE IT HELPS U ...............

Answer 2

Given,

• Ramu is twice as old as Somu.
• Five years ago his age was three times of Somu's age.

To Find,

• Present age of Ram u
• Present age of Somu.

Solution,

• Let the present age of Ramu be x years
• Let the present age of Somu be y years.

As per first condition,

• Ramu is twice as old as Somu.

Representing mathematically,

x = 2y           → (1)

As per second condition,

• Five years ago his age was three times of Somu's age.

Ages 5 years ago,

• Ramu's age = x - 5 years
• Somu's age = y - 5 years

Representing mathematically,

x - 5 = 3 ( y - 5)

⇒ x - 5 = 3y - 15

⇒ x - 3y = - 15 + 5

⇒ x - 3y = - 10           → (2)

Substituting the value of x in (2),

2y - 3y = - 10

⇒ - y = - 10

⇒ y = 10

Substitute value of y in (1),

x = 2y

⇒ x = 2 × 10

⇒ x = 20

Therefore,

• Present age of Ramu = x = 20 years
• Present age of Somu = y = 10 years

Verification,

For first case,

Ramu is twice as old as Somu.

Present age of Ramu = x = 20 years

Present age of Somu = y = 10 years

⇒ x = 2y

⇒ 20 = 2 (10)

⇒ 20 = 20

LHS = RHS.

For second case

• Five years ago his age was three times of Somu's age

Ages 5 years ago,

• Ram's age = x - 5 = 20 - 5 = 15 years
• Somu's age = y - 5 = 10 - 5 = 5 years

⇒ x - 5 = 3 ( y - 5)

⇒ 15 = 3 ( 5 )

⇒ 15 = 15

LHS = RHS.

Hence verified.....