The ratio of the ages of father and son at present is 6: 1. After 5 ye

1.	The ratio of the ages of father and son at present is 6: 1. After 5 years the ratio will become 7:2. Find the present age of the son?
Answer» ong>Answer: The present age of the son is 5 years. Step-by-step-explanation: We have given that, The ratio of the present AGES of father and son is 6 : 1. Let the common multiple be X. ∴ Father's present age = 6x years And son's present age = x years Now, After 5 years, father's age = ( 6x + 5 ) years And after 5 years, son's age = ( x + 5 ) years From the given condition, $\displaystyle{\sf\:\dfrac{(\:6x\:+\:5\:)}{(\:x\:+\:5\:)}\:=\:\dfrac{7}{2}}$ $\displaystyle{\implies\sf\:2\:\times\:(\:6x\:+\:5\:)\:=\:7\:\times\:(\:x\:+\:5\:)}$ $\displaystyle{\implies\sf\:12x\:+\:10\:=\:7x\:+\:35}$ $\displaystyle{\implies\sf\:12x\:-\:7x\:=\:35\:-\:10}$ $\displaystyle{\implies\sf\:5x\:=\ 25}$ $\displaystyle{\implies\sf\:x\:=\:\cancel{\dfrac{25}{5}}}$ $\displaystyle{\implies\underline{\boxed{\red{\sf\:x\:=\:5\:}}}}$ ∴ The present age of the son is 5 years.