Question

Rohan's mother is 26 years older then him. the product of their ages 3 years from now will be 306 we would like to find Rohan's present age​

Answer 1

C O R R E C T Q U E S T I O N :

• Rohan's mother is 26 years older then him. the product of their ages 3 years from now will be 360 we would like to find Rohan's present age

G I V E N :

• Rohan's mother is 26 years older then him. the product of their ages 3 years from now will be 360.

T O F I N D :

• Rohan's present age = ?

S O L U T I O N :

Let Rohan's age be x years and his mother's age be x + 26 years.

❍ After 3 years :

• Age of Rohan = x + 3 years
• Age of his mother = x + 26 + 3 = x + 29 years

★ According to Question :

→ (x + 3) (x + 29) = 360

→ x² + 29x + 3x + 87 = 360

→ x² + 32x + 87 - 360 = 0

→ x² + 32x - 273 = 0

By splitting middle term we get :

→ x² + 39x - 7x - 273 = 0

→ x(x + 39) - 7(x + 39) = 0

→ (x - 7) (x + 39) = 0

→ x = 7 or x = -39

As we know that we cant calculate age in negative. So, x = 7

→ x = 7

Hence,

• Present Age of Rohan = x = 7 years
• Present Age of his mother = x + 26 = 7 + 26 = 33 years

Answer 2

Correct question:

Rohan's mother is 26 years older then him. the product of their ages 3 years from now will be 360. Find Rohan's present age.

Answer:

★ Rohan's present age = 7 years ★

Step-by-step explanation:

Given:

• Rohan's mother is 26 years older than him.
• The product of their ages 3 years from now will be 360.

To find:

• Rohan's present age.

Solution:

Let the present age of Rohan be x years.

According to the 1st condition,

• Rohan's mother is 26 years older than him.

Then the age of Rohan's mother = (x+26) years

According to the 2nd condition,

• The product of their ages 3 years from now will be 306.

After 3 years,

• Age of Rohan = (x+3) years
• Age of Rohan's mother = (x+26+3) years = (x+29) years

$\implies\sf{Rohan's\:age\times\: Rohan's\: mother's\:age=360}$

$\implies$(x+3)×(x+29)=360

$\implies$ x² +29x+3x+87=360

$\implies$ x²+32x= 273

$\implies$ x² +32x-273=0

$\implies$ x² +32x-273=0

$\implies$ (x+39) (x-7)=0

Either,

x+39=0

→ x = -39 [Impossible]

Or,

x-7=0

→ x=7

Hence, the present age of Rohan is 7 years.