question_answer 23)

                Shobo's mother's present age is six times Shobo's present age. Shobo's age five years from now will be one third of his mother's present age. What are their present ages?

Answer:

                Let the present age of Shobo be \[x\] year Then, Shobo's mother's present age \[=6x\] years Five years from now Shobo's age \[=(x+5)\]years            According to the question, \[x+5=\frac{1}{3}\,(6x)\] \[\Rightarrow \]               \[x+5=2x\] \[\Rightarrow \]               \[5=2x-x\]                           |Transposing x to RHS \[\Rightarrow \]               \[5=x\] \[\Rightarrow \]               \[x=5\] \[\Rightarrow \]               \[6x=6\times 5=30\] Hence, their present ages are 5 years and 30 year Check:  \[30=5\times 6\] \[5+5=10\] \[10=\frac{1}{3}\,(30)\] Hence, the result is verified.