Question 636780
Let
Present age of mother = m years old
Present age of father = f years old
Present age of John = j years old


Two years hence
mother will be = m+2 years old
John will be = j+2 years old
Then
mother will be twice his age
m+2=2(j+2)
m+2=2j+4
m=2j+4-2
m=2j+2.................(1)



Five years hence
father will be = f+5 years old
John will be = j+5 years old
Then
father will be thrice his present age
f+5=3(j+5)
f+5=3j+15
f=3j+15-5
f=3j+10..................(2)


the sum of all the three ages is 105
m+j+f=105
Put the value of m and f from (1) and (2) to above equation
2j+2+j+3j+10=105
6j+12=105
6j=105-12
6j=93
6j/6=93/6
j=31/2
Put the value of j in (1)
m=2j+2.................(1)
m=2(31/2)+2
m=31+2
m=33

Put the value of j in (2)
f=3j+10..................(2)
f=3(31/2)+10
f=93/2+10
f=(93+20)/2
f=113/2
f=56.5

Difference b/w parents ages = f-m=56.5-33= 23.5 years.