[x:y=2:1(2)/(3);y:z=2(2)/(3);4;z:A=3;5(3)/(4)],[" If "A" 's imestonent is "746,230" ,then find "x" s invest "],[" ment."]

The ratio of inverstments of four businessmen is as follows: XY=2:1(2)/(3),Y:Z=2(2)/(3):4,Z:A=3:5(3)/(4) If A's inverstment is ₹ 46230, find X's investment.

If 2x = 3y = 4z, find x:y: z.

If x = 1, y = 2, z = 5 , then find the value of 3x – 2y + 4z.

x+y+z=1 x-2y+3z=2 5x-3y+z=3

Let S be the set of all column matrices [b_1b_2b_3] such that b_1,b_2, b_3 in R and the system of equations (in real variable) -x+2y+5z=b_1 2x-4y+3z=b_2 x-2y+2z=b_3 has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for each [b_1b_2b_3] in S? (a) x+2y+3z=b_1, 4y+5z=b_2 and x+2y+6z=b_3 (b) x+y+3z=b_1, 5x+2y+6z=b_2 and -2x-y-3z=b_3 (c) -x+2y-5z=b_1, 2x-4y+10 z=b_2 and x-2y+5z=b_3 (d) x+2y+5z=b_1, 2x+3z=b_2 and x+4y-5z=b_3

The lines (x-1)/(a) = (y-2)/(3) = (z-3)/(4) , (x-2)/(3) = (y-3)/(4) = (z-4)/(5) are coplanar. Then a=

If x:y=2:3 , y:z=3:4 , z:k=1:2 , find the value of x:y:z:k