State 1) True or 1) 2) False:
A girl is twice as old as her sister. Four years hence, the product of their ages (in years) will be 160. Their present ages are 6 years and 12 years.

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True

2) False

answer is A.

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Detailed Solution

Let the girl be twice her current age = 2x
So let her sister's age be x.
The answer to the query is:

\Rightarrow (2 x + 4) (x + 4) = 160

\Rightarrow {2 x}^{2} + 8 x + 4 x + 16 = 160

\Rightarrow {2 x}^{2} + 12 x + 16 - 160 = 0

\Rightarrow {2 x}^{2} + 12 x - 144 = 0

\Rightarrow 2 (x^{2} + 6 x - 42) = 0

\Rightarrow x^{2} + 6 x - 72 = 0

\Rightarrow x^{2} + 12 x - 6 x - 72 = 0

\Rightarrow x (x + 12) - 6 (x + 12) = 0

\Rightarrow (x + 12) (x - 6) = 0

\Rightarrow x + 12 = 0 and x - 6 = 0

∴ x = - 12 and x = 6

Age is not a negative thing.

∴ x = 6

\Rightarrow 2 x = 2 \times 6 = 12

Currenty, the present ages of both girls are 6 years and 12 years.

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