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A and B are friends and their agesdiffer by 2 years A's father D is twiceas old as A and B is twice as old as hissister c theageof D and C differ by 40years. find the ages ofA and BA |
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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 =y/2 years Clearly, D is older than C 2x− y/2 =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=82/3 = 27⅓ Putting x= 82/3 in equation (iii), we get y= 82/3 +2=88/3 =29 ⅓ Hence, A's age =26 years and B's age =24 years or A's age =27 ⅓ years and B's age =29 ⅓ years. |
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