A grandfather is ten times older than his granddaughter. He is also 54 years older than her. Find their present age.

Solution

Let the present age of granfather = x years

∴       Present age of granddaughter = $space space x over 10$ years
According to the condition, we have
      [Present age of granddaughter] + 54 = x
or                                       $space space x over 10 plus 54 equals x$
   Transposing 54 to RHS and x to LHS, we have

                   $x over 10 minus x equals negative 54$
or $fraction numerator x minus 10 x over denominator 10 end fraction equals negative 54$
or $fraction numerator negative 9 x over denominator 10 end fraction equals negative 54$
or     $negative 9 x space equals negative 54 cross times 10$         [Multiplying both sides by 10]
or     $x equals fraction numerator negative 54 cross times 10 over denominator negative 9 end fraction$               [Dividing both sides by -9]

or                       $x equals 6 cross times 10 equals 60$
and                       $x over 10 equals 60 over 10 equals 6$