question_answer 28)

                Aman's age is three times his son's age. Ten years ago he was five times his son's age. Find their present ages.

Answer:

                Let the present age of son be \[x\] years Then, the present age of Aman \[=3x\] years Ten years ago Age of Aman \[=(3x-10)\] years Age of son \[=(x-10)\]) years According to the question, \[3x-10=5(x-10)\] \[\Rightarrow \]               \[3x-10=5x-50\] \[\Rightarrow \]               \[-10+50=5x-3x\]                             | Transposing \[3x\] to RHS and ? 50 to LHS \[\Rightarrow \]               \[40=2x\] \[\Rightarrow \]               \[2x=40\] \[\Rightarrow \]               \[x=\frac{40}{2}\,=20\] | Dividing both sides by 2 \[\Rightarrow \]               \[3x=3\times 20=60\] Hence, the present ages of Aman and his son are 60 years and 20 years respectively. Check:  \[60=3\times 20\] \[60-10=50\] \[20-10=10\] \[50=10\times 5\] Hence, the result is verified.