Respuesta :
Answer : The weight of first bar is, 1 kg
Explanation :
Let the weight of first bar and second bar be, x and y.
The ratio of gold and silver in first bar is, 2 : 3
The ratio of gold and silver in second bar is, 3 : 7
The final ratio of gold and silver in first and second bar is, 5 : 11
Total weight of bar = 8 kg
The equations will be:
[tex]\frac{2}{5}x+\frac{3}{10}y=\frac{5}{16}\times 8[/tex] ..........(1)
[tex]\frac{3}{5}x+\frac{7}{10}y=\frac{11}{16}\times 8[/tex] ..........(2)
Solving both the equations, we get:
[tex]4x+3y=25[/tex] ..........(3)
[tex]6x+7y=55[/tex] ..........(4)
Now we are multiplying equation 3 by 6 and equation 4 by 4, we get:
[tex]24x+18y=150[/tex] ..........(5)
[tex]24x+28y=220[/tex] ..........(6)
Now we are subtracting equation 5 from 6, we get the value of 'y'.
y = 7
Now put the value of 'y' in equation 5, we get the value of 'x'.
x = 1
Thus, the weight of first bar and second bar is, 1 kg and 7 kg respectively.
