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A and B are the freinds and their ages differ by 2 years. A is father D is twice as old as A and B is as old as his sister C. The age of D and C differ by 40 years. Find the ages of A and B |
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Answer» Answer: LET the ages of A and B be x and y YEARS respectively. Then, x−y=±2 [Given] D's age =2x years and, C's age = 2 y
years. Clearly, D is older than C 2x− 2 y
=40⇒4x−y=80 Thus, we have the following two systems of linear equations x−y=2 .(i) and, 4x−y=80 (ii) or x−y=−2 (iii) and, 4x−y=80 ..(IV) Substracting equation (i) from equation (ii), we get 3x=78⇒x=26Putting x=26 in equation (i), we get y=24 or Substracting equation (iv) from equation (iii), we get −3x=−82⇒x= 3 82
=27 3 1
PUTTING x= 3 82
in equation (iii), we get y= 3 82
+2= 3 88
=29 3 1
Hence, A's age =26 years and B's age =24 years or A's age =27 3 1
years and B's age =29 3 1 ∘
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