There are two bars of gold-silver alloy. The first bar has 2 parts of gold and 3 parts of silver, and the other has 3 parts of gold and 7 parts of silver. If both bars are melted into an 8 kg bar with the final ratio of 5:11 (gold to silver), what was the weight of the first bar?

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:

      ..........(1)

      ..........(2)

Solving both the equations, we get:

      ..........(3)

      ..........(4)

Now we are multiplying equation 3 by 6 and equation 4 by 4, we get:

      ..........(5)

      ..........(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.