Question

rohan's mother is 26 years older than him. the product of their ages (in years) 3 years from now will be 360. we need to find rohan's present age​

Answer 1

In Present

Let Rohan Age=x years

Then Mother Age=(x+26) years

After 3 years

Rohan Age=(x+3) years

Mother Age=(x+26+3) years

Product=360 years

A/Q

(x+3)(x+26+3)=360

(x+3)(x+29)=360

x²+29x+3x+87=360

x²+32x+87=360

x²+32x+87-360=0

x²+32x-273=0

By Middle Term Spilliting

x²+(39-7)x-273=0

x²+39x-7x-273=0

x(x+39)-7(x+39)=0

=(x-7)(x+39)=0

A/Q

x-7=0

x=0+7

x=7

x+39=0

x=0-39

x=-39

Hence Age Can't be in negative

x=7 years

Rohan Age=x=7 years

Mother Age=x+26=7+26=33 years

$\boxed{\mathtt{\huge{Rohan=7\: years}}}$

$\boxed{\mathtt{\huge{Mother=33\: years}}}$

Answer 2

$\rule {200}{2}$

Answer :-

Explanation :-

Let, Rohan's present age be x years.

So, according to the question, we can say that her mother's age would be (x + 26) years

After 3 years, Rohan's age = x + 3

Her mother's age would be = x + 26 + 3 = x + 29 years.

Given, their product is 360

→ (x + 3)(x + 29) = 360

→ x² + 29x + 3x + 87 = 360

→ x² + 32x + 87 - 360 = 0

→ x² + 32x - 273 = 0

→ x² + 39x - 7x - 273 = 0

(By splitting the middle terms)

→ x(x + 39) - 7(x + 39) = 0

→ (x - 7)(x + 39) = 0

→ (x - 7) = 0/(x + 39)

→ x - 7 = 0

→ x = 7

Similarly, x = -39

But, age cannot be negative, hence x = 7 years.

So, present age of Rohan is 7 years.

$\rule {200}{2}$