question_answer 27)

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

Answer:

                Let the present age of grand daughter be \[x\] years Then, the present age of grandfather is \[10x\] years According to the question, \[10x=x+54\] \[\Rightarrow \]               \[10x-x=54\]                      | Transposing \[x\] to LHS \[\Rightarrow \]               \[9x=54\] \[\Rightarrow \]               \[x=\frac{54}{9}=6\]                       | Dividing both sides by 9 \[\Rightarrow \]               \[10x=10\times 6=60\] Hence, their present ages are 60 years and 6 years Check:  \[60=6\times 10\] \[60=6+54\] Hence, the result is verified.