Mathematics
The ages of two sisters are 11 years and 14 years. In how many years time will the product of their ages be 304 ?
Answer
Let in x years the product of their ages be 304.
In x years age of sisters will be (11 + x) and (14 + x).
∴ (11 + x)(14 + x) = 304
⇒ 154 + 11x + 14x + x2 = 304
⇒ x2 + 25x + 154 - 304 = 0
⇒ x2 + 25x - 150 = 0
⇒ x2 + 30x - 5x - 150 = 0
⇒ x(x + 30) - 5(x + 30) = 0
⇒ (x - 5)(x + 30) = 0
⇒ x - 5 = 0 or x + 30 =0
⇒ x = 5 or x = -30.
Since time cannot be negative,
∴ x ≠ -30.
Hence, in 5 years the product of age of sisters will be 304.
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