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4. Vivek is older than Kishor by 5 years. The sum of the reciprocals of their ages is \(1\over 6\) . Find their present ages.

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Sol.    Let the present age of Kishor be \(x \) years
∴       Present age of Vivek (\(x \) + 5) years
          According to the given condition,

∴        \({1\over x }+{1\over x+5}\)         =  \(1\over 6\) 

∴        \(x+5+x\over x(x+5)\)            =  \(1\over 6\)

∴        \(2x+5\over x^2+5x\)             =  \(1\over 6\)

∴        \(x^2\)    +    5\(x \)      =   6(2\(x \) + 5)
∴        \(x^2\)    +    5\(x \)      =   12\(x \) + 30
∴ \(x^2\) + 5\(x \) – 12\(x \) – 30 =  0
∴           \(x^2\) – 7\(x \) – 30  =  0

                            


∴  \(x^2\) – 10\(x \) + 3\(x \) – 30 =  0
∴ \(x \)(\(x \) – 10) + 3(\(x \) – 10) = 0
∴     (\(x \) – 10)  (\(x \) + 3)     = 0
∴    \(x \) – 10 = 0   or   \(x \) + 3  =  0
∴           \(x \)  = 10 or          \(x \) = –3
\(x \) = –3 is not acceptable because, age can not be negative


Present age of Kishor is 10 years and present age of Vivek is = 10 + 5 = 15 years

uÉaÉïxÉqÉÏMüUhÉ August 10 , 2018 0 Comments 10 views