Question

two lumps of gold, silver and copper together weigh 20kg. one lump contains 75% gold and 31.25 grams silver per kilogram. another lump contains 85% gold and 30 grams silver per kilogram. the total quality of silver in two lumps is 617.5 grams. if two lumps are melted to form one, the percentage of gold in it will be: 75% 15.6% 87% 78%

Answer 1

Answer: The correct answer is 78%

Explanation:

Total weight of silver in both lumps = 617.5 g = $\frac{617.5}{1000}kg$

let the weight of one lump be X kg and thus the weight of another will  be (20-X)kg as total weight is 20 kg

For lump 1

weight of gold = 75% of  X kg

weight of silver = 31.25 g/kg

1 kg of lump 1 have 31.25 g of silver

X kg of lump1 will have=$31.25\times X g=\frac{31.25X}{1000}kg$

For lump 2

weight of silver = 30 g/kg

1 kg of lump 2 contains 30 g of silver

(20-X) kg of lump 2 contains silver=  $=30\times (20-X)g=\frac{30(20-X)}{1000}kg$

Total weight of silver = weight of silver in lump1 + weight of silver in lump 2

$\frac{617.5}{1000}kg=\frac{31.55X}{1000}kg+\frac{30(20-X)}{1000}kg$

solving for X,we get

X = 14 kg

so, lump 1 weighs =14kg

    lump 2 weighs = (X-14)=(20-14)=6kg

weight of gold in lump 1 $(w_1)$

= 75% of 14kg = $\frac{75}{100}\times 14$ = 10.5kg

weight of gold in lump 2 $(w_2)$

= 85% of 6kg = $\frac{85}{100}\times 6$ = 5.1kg

$\text{Percentage of Gold after the lumps are melted into one}$

$=\frac{w_{1}+w_{2}}{total weight of lumps}\times{100}=\frac{10.5+5.1}{20}\times 100$

Percentage of Gold after the lumps are melted into one = 78%