Question

Sohan's mother is 20 years older than him. the product of their ages 5 years from now will be 300 . find sohan's present age​

Answer 1

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.

Answer 2

Let age of Sohan be = x years

Mother = x + 20 years

After 5 years, their ages are:

• Sohan = x + 5 years
• Mother = x + 20 + 5 = x + 25 years

Product of their ages = (x + 5)(x + 25) = 300

Solve this equation now, and get the answer.

=> x^2 + 25x + 5x + 125 = 300

=> x^2 + 30x + 125 = 300

=> x^2 + 30x - 175 = 0

Use the quadratic formula for easier way:

Formula: x = (-b ± √b^2 - 4ac)/2a

Where, a = 1, b = 30, c = -175

=> x = (-30 ± √900 + 700)/2

=> x = (-30 ± √1600)/2

=> x = (-30 ± 40)/2

=> x = (-30 - 40)/2 , (-30 + 40)/2

=> x = -70/2 , 10/2

=> x = -35 , 5

Since age ≠ negative, x = 5 years.

Sohan = 5 years

Mother = 25 years