An ornament weighing 50 g in air weighs only 46 g in water. Assuming that some copper is mixed with gold to prepare the ornament. Find the amount of copper in it. Specific gravity of gold is 20 and that of copper is 10.

Sure, let's solve this step by step.

1. First, we need to find the volume of the ornament. We can do this using Archimedes' principle, which states that the buoyant force (or upthrust) on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. In this case, the weight of the ornament in air minus its weight in water will give us the weight of the water displaced by the ornament, which is equal to the volume of the ornament (since the density of water is 1 g/cm³). So, the volume of the ornament is 50 g - 46 g = 4 cm³.

2. Next, we need to find the weight of gold and copper in the ornament. We know that the ornament is made of gold and copper, and we know the specific gravities of gold and copper. The specific gravity of a substance is the ratio of the density of the substance to the density of water. Since the density of water is 1 g/cm³, the densities of gold and copper are 20 g/cm³ and 10 g/cm³, respectively.

3. Let's assume that the weight of the gold in the ornament is G g and the weight of the copper is C g. Since the total weight of the ornament is 50 g, we have G + C = 50.

4. We also know that the total volume of the ornament is the sum of the volumes of the gold and copper in it. The volume of a substance is equal to its weight divided by its density. So, the volume of the gold is G/20 cm³ and the volume of the copper is C/10 cm³. Since the total volume of the ornament is 4 cm³, we have G/20 + C/10 = 4.

5. Now we have a system of two equations, and we can solve it to find the values of G and C. Multiplying the second equation by 20 gives us G + 2C = 80. Subtracting the first equation from this gives us C = 30. Substituting C = 30 into the first equation gives us G = 20.

So, the ornament contains 20 g of gold and 30 g of copper.