Question

Priyanka's mother is 20 years older than her.The product of their ages 5 years from now will be 300 we would like to find priyanka's present age keep it in mind,construct the quadratic equation.

Answer 1

Solution :-

Let :-

Present age of Priyanka = x

Present age of Priyanka's mother = y

After 5 years :-

Age of Priyanka = x + 5

Age of Priyanka's mother = y + 5

According to the first condition :-

$\longrightarrow \sf y = x+20 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..........................(1)$

According to the second condition :-

$\longrightarrow \sf (x+5)(y+5) = 300 \\\\\longrightarrow xy+5x+5y+25 = 300 \\\\\longrightarrow xy+5x+5y = 275 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..........................(2)$

Substitute the value of y in eq (2) :-

$\longrightarrow \sf x(x+20)+5x+5(x+20) = 275 \\\\\longrightarrow x^2+20x+5x+5x+100 = 275 \\\\\longrightarrow x^2+30x = 175 \\\\\longrightarrow x^2+30x-175 = 0 \\\\\longrightarrow x^2+35x-5x-175 = 0 \\\\\longrightarrow x(x+35)-5(x+35)= 0 \\\\\longrightarrow (x+35)(x-5)=0 \\\\\longrightarrow \bf x = -35 \ , \ x = 5$

Age cannot be negative .

So, x = 5

Present age of Priyanka = 5 years

Answer 2

Step-by-step explanation:

Gɪᴠᴇɴ :-

• Sohan's mother is 20 years older than him.

• The product of their ages 5 years from now will be 300 .

Tᴏ Fɪɴᴅ :-

• Sohan's present age ?

Sᴏʟᴜᴛɪᴏɴ :-

Let us Assume That, Sohan Present age is X years.

Than,

→ Sohan's mother Age = (x + 20) Years.

And, 5 Years from Now :-

→ Sohan will be = (x + 5) Years old.

→ Sohan's mother will be = (x + 20) + 5 = (x + 25) Years old.

A/q ,

→ (x + 5)(x + 25) = 300

→ x² + (25+5)x + 25 × 5 = 300

→ x² + 30x + 125 - 300 = 0

→ x² + 30x - 175 = 0

→ x² + 35x - 5x - 175 = 0

→ x(x + 35) - 5(x + 35) = 0

→ (x + 35)(x - 5) = 0

→ x = (-35) or, 5 . (-ve age Not possible.)

Hence, Sohan Present age is 5 Years.