Question

a woman is 6 times as old as her son two years ago the productof their ages was84. find their present ages.

the answer is 30 years and 5 years.

please solve the problem for me.​

Answer 1

Answer:

The present ages of mother and her son are 30 years and 5 years respectively.

Step-by-step-explanation:

Let the present age of the son be x years.

∴ The present age of mother = 6x years

Now,

Age of son two years ago = ( x - 2 ) years

And age of mother two years ago = ( 6x - 2 ) years

From the given condition,

( x - 2 ) ( 6x - 2 ) = 84

⇒ x ( 6x - 2 ) - 2 ( 6x - 2 ) = 84

⇒ 6x² - 2x - 12x + 4 = 84

⇒ 6x² - 14x + 4 - 84 = 0

⇒ 6x² - 14x - 80 = 0

⇒ 6x² - 30x + 16x - 80 = 0

⇒ 6x ( x - 5 ) + 16 ( x - 5 ) = 0

⇒ ( x - 5 ) ( 6x + 16 ) = 0

⇒ ( x - 5 ) = 0 OR ( 6x + 16 ) = 0

⇒ x - 5 = 0 OR 6x + 16 = 0

⇒ x = 5 OR 6x = - 16

⇒ x = 5 OR x = - 16 / 6

Age cannot be negative.

∴ x = - 16 / 6 is not acceptable.

∴ x = 5 years

∴ Present age of son = 5 years

Now,

Present age of mother = 6x

⇒ Present age of mother = 6 * 5

⇒ Present age of mother = 30 years

∴ The present ages of mother and her son are 30 years and 5 years respectively.

Answer 2

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★ Correct Question :

• A woman is 6 times as old as her son two years ago the product of their ages was 84. find their present ages.

★ Required Answer :

• The present ages of woman and her son = 30 years and 5 years.

ㅤㅤㅤㅤㅤㅤ━━━━━━━━━━

★ Step by step explanation :

• Let the present age of her son = y years
• So, present age of woman = 6y years
• Age of son 2 years ago = (y - 2) years
• Age of mother 2 years ago = (6y - 2) years

Atq,

➠ㅤㅤㅤ(y - 2) (6y - 2) = 84ㅤㅤㅤ(Given)

➠ㅤㅤㅤy(6y - 2) - 2(6y - 2) = 84

➠ㅤㅤㅤ6y² - 2y - 12y + 4 - 84 = 0

➠ㅤㅤㅤ6y² - 14y - 80 = 0

★ By splitting the middle term :

➠ㅤㅤㅤ6y² - 30y + 16y - 80 = 0

➠ㅤㅤㅤ6y (y - 5) + 16 (y - 5) = 0

➠ㅤㅤㅤ(6y + 16) (y - 5) = 0

➠ㅤㅤㅤ6y + 16 = 0 , y - 5 = 0

➠ㅤㅤㅤ6y = -16 , y = 5

➠ㅤㅤㅤy = -16/6 , y = 5

Age can't be negative !!

So, we will reject y = -16/6

ㅤㅤㅤㅤㅤㅤ━━━━━━━━━━

Now,

★ Present age of woman :

➠ㅤㅤㅤ6y = 6 × 5 = 30 years

∴ Present ages of woman and her son = ㅤ30 years and 5 years

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