The sum of their (father, mother and son) ages is 70. The father is 6 times as old as the son.When the sum of their ages is twice 70, the father will be twice as old as the son.How old is the mother?

• let present ages of father, mother and son are F,M, S.
  Then F+M+S = 70 where F= 6S
  Then M+7S= 70
  
  After x years , sum of ages will be twice 70 means 140 years.
  it means 3 x= 70 ; x= 70/3 years.
  
  At that time ages of father, mother and son will be F+ 70/3, M+70/3 and S+70/3 years. and F+70/3 = 2*(S+70/3)
  hence 6S+70/3 = 2*(S+70/3)
  4S= 70/3
  S= 70/12 = 35/6 years
  F= 35 years .
  Mother = 70-35-35/6 = 35-35/6 = (210-35)/6 = 175/6 years = 29 years 2 months
• 12 years agoHelpfull: Yes(2) No(3)
• Answer: 29yrs
  Ratio of present ages of father n son is 6:1
  Sum of present ages of F+S+M=70——————(1)
  After x yrs ages will be in the ratio 2:1
  Sum of ages after x yrs is F+x+S+x+M+x=140
  70+3x=140, from (1)
  x=70/3, so after 70/3 yrs father’s age wil be double of his son
  (We can do a mental calculation to solve this part, after x yrs, sum of their ages increases 3x, and change in sum of age is 70, 3x=70)
  
  6:1
  2:1 70/3
  
  70/3*(2-1)/(6-2)
  70/3*1/4=35/6
  
  Father’s age = 6*35/6=35
  Son’s age= 35/6= 6, (5.8 can be rounded to 6)
  Mother’s age= 70-(35+6), from (1) sum of ages is 70
  = 70-41=29 yrs
• 5 years agoHelpfull: Yes(0) No(0)