Question

Two alloys composed of gold and silver together weight 20 kg. One lump contains 75% gold and 31.25 gm per kg silver. Another alloy contains 85% gold and 30 gm per kg silver. The total quantity of silver in two lumps is 617.5 gm. If the two lumps are melted and formed into one, what percentage of gold will it contain?

Answer 1

Answer:

We have two lumps having mixture of gold and silver weighing 20 Kg.

So , let x be the amount of first lump melted to form one with second one.

So we have x + y = 20........(1)

We have 31.25 gm silver per kg in first lump and 30 gm silver per kg in second lump.

And total silver given is 617.5gm

So our second equation is 31.25x + 30y = 617.5..........(2)

Putting value of x from equation (1) in (2)

We get 1.25y = 7.5

or, y = 6

Therefore x will be 20-6 which is 14

Now we have 75% gold in first lump.

So total gold in first lump is 75/100*x

Now we have 85% gold in second lump .

So total gold in second lump is 85/100*y

So total gold in the melted mixture is 75/100*x + 85/100*y

                                                            = 75/100*14 + 85/100*6

                                                            = 15.6 Kg

So percentage of gold in the final mixture will be 15.6/20*100

                                                                                 =78%

Hope this helps!!!

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