Question

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

Answer 1

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%.