Question

A king ordered that a golden crown be made for him from 8 kg of gold and 2 kg of silver and crown when made weighed 10 kg . Archimedes knew that under water gold lost 1/20th of its weight while silver lost 1/10th .when crown was weighed under water it was 9.25 kg .how much gold was stolen by goldsmith?​

Answer 1

The quantity of gold stolen by goldsmith is 3 Kilograms.

Let us consider the amount of gold in crown be 'X'.

Let us consider the amount of silver in the crown to be 'Y'.

By given condition, X+Y=10 in air.Let this be our first equation.

But under water gold loses 1/20 of its quantity and silver loses 1/10 of its quantity.

So in underwater the loss in the weight of gold and silver become X/20 and Y/10 respectively.

The weight of crown in water ,by given condition is (X-(X/20))+(Y-(Y/10)) = 9.25.

This equation can also be written as (19X/20)+(9Y/10)=9.25.

This can be further modified into (19X+18Y=185).(This is obtained by multiplying common multiple 20 in both sides)

Let this be our second equation.

The equation of weight of crown in air,ie. the first equation ,can be modified as 19X+19Y=190.

By solving first and second equation we get y=5 and x=5.

That is the amount of gold in crown X=5Kg, and silver Y=5Kg.

So to find out the quantity of gold stolen by goldsmith we subtract the Total gold in the Crown from the quantity of gold the king gave the goldsmith to make the crown.

Total gold given by King or Total gold the Crown is to be made of =8Kg.

The amount of gold present in the crown = 5Kg.

The amount of gold stolen by goldsmith is 8-5Kg= 3Kg.

Answer 2

The gold that stolen by goldsmith is 3 Kgs.

Step-by-step explanation:

Solution:

Gold : silver = 8 : 2

Under water, weight lost by gold = $\frac{1}{20} \times 8$ = 0.4 kg

Weight lost by silver = $\frac{1}{10} \times 2$ = 0.2 kg

The total weight has to be = 10 – (0.4 + 0.2) = 9.4

Under water the crown weight 9.25 kg,  

The difference in weight = 9.4 – 9.25 = 0.15 kg

The gold stolen by him = 0.15 $\times$ 20 = 3 Kgs

To know more:

If one gold bangle is made from 12 gms 250miligrams of gold how much gold will be needed to make 8 such bangles.

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