The sum of present ages of 3 persons is 72 yrs. Seven years ago,...

Given: The sum of present ages of 3 persons $=72$ years Seven years ago, their ages were in the ratio $4: 6: 7$ Formula Used: Sum of present ages $=x+y+z$ Ratio relation: $(x-7):(y-7):(z-7)=4: 6: 7$ Calculation: Let the ages of three persons seven years ago be (4 $\mathrm{k},$6 $\mathrm{k}$), and 7 k respectively. Then, their present ages are $(4 k+7),(6 k+7)$, and $(7 k+7)$. According to the given condition: ($$\begin{aligned} & (4 \mathrm{k}+7)+(6 \mathrm{k}+7)+(7 \mathrm{k}+7)=72 \\ & \Rightarrow 4 \mathrm{k}+6 \mathrm{k}+7 \mathrm{k}+21=72 \\ & \Rightarrow 17 \mathrm{k}+21=72 \\ & \Rightarrow 17 \mathrm{k}=72-21 \\ & \Rightarrow 17 \mathrm{k}=51 \\ & \Rightarrow \mathrm{k}=51 / 17 \\ & \Rightarrow \mathrm{k}=3 \end{aligned}$$) So, their present ages are: (4 $\mathrm{k}+$7=4 \times 3+7=12+7=19) years (6 k+7=6 \times 3+7=18+7=25) years (7 k+7=7 \times 3+7=21+7=28) years The present ages are 19, 25, and 28 years.