The product of the ages of two sisters is 104. The difference between

1.	The product of the ages of two sisters is 104. The difference between their ages is 5. Find their ages.
Answer» Let the sister and her sister’s age be ‘X’ yrs and ’(X+5)’ yrs respectively. As per the question, X(X + 5) = 104 X² + 5X – 104 = 0 X² + 13X – 8X + 132 = 0 X(X + 13) – 8(X + 13) = 0 (X + 13)(X – 8) = 0 ∴ X = 8 or X = –13 The ages of sisters are 8 years & 13 years respectively, as the age can’t be negative.

The product of the ages of two sisters is 104. The difference between their ages is 5. Find their ages.

Answer»

Let the sister and her sister’s age be ‘X’ yrs and ’(X+5)’ yrs respectively.

As per the question,

X(X + 5) = 104

X² + 5X – 104 = 0

X² + 13X – 8X + 132 = 0

X(X + 13) – 8(X + 13) = 0

(X + 13)(X – 8) = 0

∴ X = 8 or X = –13

The ages of sisters are 8 years & 13 years respectively, as the age can’t be negative.