Age of family

The age of father and son is in the ratio 10: 3. The age of the father and daughter is in ratio 5: 2. How old are a father and a son if the daughter is 20?

Result

o =  50
s =  15

Solution:

o:s=10:3 o:d=5:2 d=20  o=52 d=52 20=50o:s=10:3 \ \\ o:d=5:2 \ \\ d=20 \ \\ \ \\ o=\dfrac{ 5 }{ 2 } \cdot \ d=\dfrac{ 5 }{ 2 } \cdot \ 20=50
s=310 o=310 50=15   Correctness test:  p1=o/s=50/151033.3333 p2=o/d=50/20=52=2.5s=\dfrac{ 3 }{ 10 } \cdot \ o=\dfrac{ 3 }{ 10 } \cdot \ 50=15 \ \\ \ \\ \text{ Correctness test: } \ \\ p_{1}=o/s=50/15 \doteq \dfrac{ 10 }{ 3 } \doteq 3.3333 \ \\ p_{2}=o/d=50/20=\dfrac{ 5 }{ 2 }=2.5



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