Gold is 19 times as heavy as water and copper 9 times. In what ratio should these     metals be mixed so that the mixture may be 15 times as heavy as water?Options :1 : 23 : 22 : 34 : 5

This problem can be solved using the concept of weighted averages.

Let's denote:

• the ratio of gold to copper in the mixture as G : C
• the weight of gold as 19 (since gold is 19 times as heavy as water)
• the weight of copper as 9 (since copper is 9 times as heavy as water)
• the weight of the mixture as 15 (since the mixture is 15 times as heavy as water)

According to the rule of alligation (a rule that allows us to find the ratio in which two or more ingredients at given prices must be mixed to produce a mixture of a desired price), the ratio G : C can be found as follows:

1. Subtract the weight of the mixture from the weight of each metal to find the differences:

   • For gold: 19 - 15 = 4
   • For copper: 15 - 9 = 6

2. The ratio G : C is then given by these differences: 4 : 6

3. Simplify the ratio by dividing each number by the greatest common divisor (in this case, 2): 4/2 : 6/2 = 2 : 3

So, the metals should be mixed in the ratio 2 : 3. Therefore, the correct option is 2.

This problem can be solved using the concept of weighted averages.

Let's denote the amount of gold as G and the amount of copper as C.

We know that gold is 19 times as heavy as water and copper is 9 times. So, the total weight of the mixture is 19G + 9C.

We also know that the mixture is 15 times as heavy as water. So, the total weight of the mixture is also 15(G + C).

Setting these two expressions equal to each other gives us:

19G + 9C = 15G + 15C

Solving this equation for G/C gives us the ratio of gold to copper in the mixture.

Rearranging the terms, we get:

4G = 6C

So, G/C = 6/4 = 3/2

Therefore, the metals should be mixed in the ratio 3:2.

So, the correct option is 2.

This problem can be solved using the method of Allegation, which is a rule of mixture to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of a desired price.

Here, the mean price is 15 (the mixture is 15 times as heavy as water).

The cheaper price is 9 (copper is 9 times as heavy as water).

The dearer price is 19 (gold is 19 times as heavy as water).

Using the formula of Allegation:

(Mean Price - Cheaper Price) : (Dearer Price - Mean Price)

We get:

(15 - 9) : (19 - 15)

Which simplifies to:

6 : 4

This can be further simplified to:

3 : 2

So, the metals should be mixed in the ratio 3:2 (Gold:Copper) to get a mixture that is 15 times as heavy as water. Therefore, the correct option is 2.

This problem can be solved using the method of Allegation, which is a rule of mixture to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of a desired price.

Here, the mean price is 15 (the mixture is 15 times as heavy as water), the cheaper price is 9 (copper is 9 times as heavy as water), and the dearer price is 19 (gold is 19 times as heavy as water).

The formula for Allegation is:

(Mean Price - Cheaper Price) : (Dearer Price - Mean Price)

Substituting the given values into the formula, we get:

(15 - 9) : (19 - 15)

This simplifies to:

6 : 4

This ratio can be further simplified to:

3 : 2

So, the metals should be mixed in the ratio 3:2 (Gold:Copper) for the mixture to be 15 times as heavy as water. Therefore, the correct option is 2.

This problem can be solved using the method of Allegation, which is a rule of mixture to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of a desired price.

Here, the mean price is 15 (the mixture is 15 times as heavy as water).

The cheaper price is 9 (copper is 9 times as heavy as water).

The dearer price is 19 (gold is 19 times as heavy as water).

Using the formula of Allegation:

(Mean Price - Cheaper Price) : (Dearer Price - Mean Price)

We get:

(15 - 9) : (19 - 15)

Which simplifies to:

6 : 4

This can be further simplified to:

3 : 2

So, the metals should be mixed in the ratio 3:2 (Gold:Copper) to get a mixture that is 15 times as heavy as water. Therefore, the answer is option 2.