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Q.

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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a

True

b

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:
⇒  (2x+4)(x+4)=160
⇒  2x2+8x+4x+16=160
⇒  2x2+12x+16-160=0
⇒  2x2+12x-144=0
⇒  2(x2+6x-42)=0
⇒  x2+6x-72=0
⇒  x2+12x-6x-72=0
⇒  x(x+12)-6(x+12)=0
⇒  (x+12)(x-6)=0
⇒  x+12=0 and x-6=0
∴  x=-12 and x=6
Age is not a negative thing.
∴  x=6
⇒  2x=2 × 6=12
Currenty, the  present ages of both girls are 6 years and 12 years.
 
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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.