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Acceleration due to gravity g' on moon is 1/6 times acceleration due to gravity g on the Earth.  So weight' = mass * g'  = mass * g / 6  = Weight on earth / 6

So W' = 60 / 6 = 10 Newtons
Mass remains same.

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Weight on earth is six times as that of moon. It simply means that we will weigh 1/6 of what we weigh on earth

If our weight is 60 kg on earth then we will weigh 1/6×60=10kg.
But mass remains same.