Three friends whose ages form a G.P. divide a certain sum of money in proportion to their ages. If they do that three years later, when the youngest is half the age of the oldest, then he will receive Rs. 150/- more than he gets now, and the middle friend will get Rs. 15 more than now, then the age of the youngest friend is

Step-by-step solution

Let the age of friends be a , ar , ar ^2, r 1 and money distributed is x , xr , xr ^2 respectively. (1+r+r^2 ) x= (a (1+r+r^2 )+a ) t Also after 3 years a r^2+3=2(a+3) a (r^2-2 )=3x+105=(a+3) t and x r +15=( ar +3) t (qiven) (1+r) x+120=(a(1+r)+6) t 2(a+3) t=r^2 x-120=2 x+210 (r^2-2 ) x=330 Using (r^2-2 ) x=330, a (r^2-2 )=3 x=110 a 110 a+105=(a+3) t 5(22 a+21)=(a+3) t and 110ar +15=(a r+3) t 5(22 a r+3)=(a r+3) t and 110ar +15=(a r+3) t 5(22 a r+3)=(a r+3) t 22 a+21 22 a r+3 = a+3 a r+3 5 a r=7 a+6 Where 5ar =7 a