two lumps having mixture of gold and silver together weight 20kg . one lump contains 75% gold snd 31.25 gm silver per kg . another lump contains 85% and 30gm silver per kg . totaly quantity of silver in two lumps is 617.5 gm. of two lumps are melted to form one, then percentage of gold in it will be
Answers
Given: Two lumps having mixture of gold and silver together weight 20 kg . one lump contains 75% gold and 31.25 gm silver per kg.
To find: If two lumps are melted to form one, then percentage of gold in it?
Solution:
- Now we have given two lumps having mixture of gold and silver weighing 20 Kg.
- So , let the amount of first lump melted to form one with second one be x, then:
x + y = 20 ...............(1)
- Again we have given that 31.25 gm silver per kg in first lump and 30 gm silver per kg in second lump and total silver given is 617.5 gm, so:
31.25x + 30y = 617.5 ................(2)
- Solving (1) in (2), we get:
1.25y = 7.5
y = 7.5 / 1.25
y = 6
x = 20 - 6
x = 14
- Now we have given that 75% gold is there in first lump, so total gold in first lump will be:
(75 / 100) x = 75/100 x 14
- Now we have also given that there is 85% gold in second lump, so total gold in second lump will be:
(85/100) y = 85/100 x 6
- So total gold in the melted mixture will be :
(75 / 100) x + (85/100) y
75/100 x 14 + 85/100 x 6
15.6 kg
- So percentage of gold in the final mixture will be
(15.6 / 20) x 100
78%
Answer:
So percentage of gold in the final mixture will be 78%.