Question

How much more pure gold be added to 1KG of 14carat gold to convert it to22carat gold ?(14carat means 14parts of pure gold and 10parts of alloy )

Answer 1

Answer:

4 kg of pure gold needs to be added to 1 kg of 14-carat gold so as to obtain 22-carat gold.

Step-by-step explanation:

We have:

1 kg of 14 carat gold

Let us assume that 24 carat stands for pure gold

Hence, 14 carat gold will have (14/24) of gold by weight

Weight of gold in 1 kg of 14 carat gold = (14/24)*1 kg = 7/12 kg

We need to find how much pure gold must be added to make the mixture into 22 carat gold.

Let "x" be the required amount of pure gold added to the 1 kg of 14-carat gold.

The weight of the mixture will be (1 + x) kg

In this mixture, we need gold to in the ratio (22/24)

Currently the amount of pure gold in the mixture = 7/12 kg

When we add x amount of pure gold, the gold in the mixture will be x + (7/12)

This should be equal to (22/24) of the total mixture.

[Please note that since we are adding pure gold, the weight of both pure gold and the mixture increases by "x"]

=> (7/12) + x = (22/24)(1 + x)

=> (7 + 12x)/12 = [22(1 + x)]/24

=> (7 + 12x) = 11(1 + x)

=> 7 + 12x = 11 + 11x

=> x = 4

We will need to add 4 kg of pure gold.

Verification:

Currently the 1 kg of 14-carat gold has (14/24) kg of gold

Once we add 4 kg of gold, the total weight of the mixture will be 5 kg.

This will have (14/24) kg + 4 kg of gold = (55/12) kg of gold

The mixture of 5 kg now has (55/12) kg of gold ...(i)

5 kg of 22-carat gold will need to have (22/24)*5 kg of gold

(22/24)*5 = (11/12)*5 = 55/12

=>  5 kg of 22-carat gold will need to have (55/12) kg of gold ...(ii)

From (i) and (ii), our answer is verified.