Question

The sum of the ages of two friends is 20 years. Four years ago, the product of their
ages in years was 48. Is this situation possible? If so, determine their present ages

Answer 1

✫ Correct Question :

• ➸ The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48. Is this situation possible? If so, determine their present ages

✫ Required Solution :

✰ Given:-

• ➸ The sum of the ages of 2 friends =20

✰ Assumption :

• ➸ Let the present age of one of 2 friends be x years.

• ➸ The present age of other friend = (20-x) years

✫ 4 years Ago :

• ➸ Four years ago,the age of 2 friends were(x-4) and (16-x) years respectively.

✰ According To Question :

• ➸ (x-4) (16-x)=48

• ➸ 16x-x²-64+4x=48

• ➸ 20x-x²-64=48

• ➸ -x²+20x-64-48=0

• ➸ -x²+20x-112=0

• ➸ x ²-20x+112=0

✫ Now Comparing both sides :

• ax + bx + c = 0

✰ Values that we have :

• ➸ a = 1

• ➸ b = -20

• ➸ c = 112

✰ By Using Discriminant formula :

• ➸ b² - 4ac

• ➸ (-20)²-4(1)(112)

• ➸ 400 - 448

• ➸ - 48 < 0

✩ (no real roots exist here ) ✩

✰ Conclusion :

• ➼ we can't find the real ages of two friends !

• ➼ Finding their ages is impossible !

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Answer 2

$\huge\bold{Given :- }$

$\looparrowright$ the sum of the ages of two friends is 20 years.

$\looparrowright$let one age = x and the other age is 20 - x

$\looparrowright$After 4 years ago,

$\looparrowright$ages are (x - 4) and (20 - x - 4) = (16 - x)

$\looparrowright$Again given product of age is 48

$\looparrowright$. (x - 4)*(16 - x)=48

$\looparrowright$ 16x - x2 - 64 + 4x = 48

$\looparrowright$ -x2 + 20x -64 - 48 = 0

$\looparrowright$ -x2 + 20x - 112 = 0

$\looparrowright$ x2 - 20x + 112 = 0

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$\huge\bold{Note :-}$

$\looparrowright$ Since this equations has no real root.

$\looparrowright$ So this situation does not exist or possible.

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Thankyou :)