Question- Write the quadratic equation for the following:“The age of Ruchi is twice the age of Monika. The
product of their ages will be 160 after four years. Find their present ages.”
Answers
Let the age of Monika be x years.
A/Q , Ruchi is twice the age of Monika .
Ruchi's age = 2x .
After 4 years,
- Monika's age = x +4
- Ruchi's age = 2x + 4
A/Q , product of their ages after 4 years is 160 .
(x+4) (2x + 4) = 160
→ x ( 2x + 4) + 4(2x + 4) = 160
→ 2x² + 4x + 8x + 16 = 160
→ 2x² + 12x + 16 = 160
Dividing the equation by 2 :
→ x² + 6x + 8 = 80
Hence the required quadratic equation is :
Solving the equation :
x² + 6x + 8 = 80
→ x² + 6x +8 - 80 = 0
→ x² + 6x - 72 = 0
→ x² + ( 12 - 6) x -72 = 0
→ x² + 12x - 6 x - 72 = 0
→ x( x +12) - 6 (x + 12) = 0
→ (x-6) (x +12) = 0
x -6 = 0
→ x = 6
x +12 = 0
→ x = -12
Since age can't be negetive , ignoring the negetive value and taking x as 6 .
- Monika's present age = 6 years
- Ruchi's present age = 2× 6 = 12 years
ANSWER:
According to Problem:
Let the age of Monika be x years.
and, Ruchi's age will be 2x years.
Now,
Monika's age after 4 years = x + 4
And Ruchi's age after 4 years = 2x + 4
ATQ,
Product of their ages is 160 after 4 years.
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Divide this quadratic equation by 2
By solving this equation:
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Note: As age cannot be negative, ignore the negative value and take x as 6.
Hence,
Monika's present age = x = 6 years.
Ruchi's present age = 2x = 2 × 6 = 12 years.