The lines 2x+5y=10 and 3x+4y=12 cuts the  x-axis at  A and B respectively. A line L drawn through the point 3,4 meets  y-axis at C such that the abscissae of  A ,B,   and ordinate of C  are in geometric progression. If the equation of the line L  is ax+by+c=0 then a+b+c is

The line 2x+5y=10 cuts x-axis at A5,0 and the line  3x+4y=12  cuts  x-axis at B4,0The point C lies on   y-axis , let it be  C0,kGiven  5,4,k are in geometric progressionIt implies that 45=k4 Cross multiply  5k=16k=165Hence the line  L is passing through the points  3,4,0,165Equation of  Ly−4=165−40−3x−3=415x−315y−60=4x−124x−15y+48=0Hence, a+b+c=4−15+48=37