A lump of gold and silver weighing 100gm is `93,500; if the weights of gold and silver be interchanged, it would be worth `2,11500. If the price of silver be `50 per gm, find the weight of gold in the mixture and price of gold per gm.
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Given:
According to question we have
100gm lump in silver = x
100gm lump in gold = 100-x
price of silver = 50 per gm
price of gold = y
50x + y(100-x) = 93500
50x + 100y -xy = 93500 -(1)
Interchange value of gold and silver
50(100-x) + (x)y = 211500
5000 - 50x + xy = 211500 -(2)
By adding 1 and 2
50x +100y - xy + 5000 -50x + xy = 93500 + 211500
5000 + 100y = 305000
100y = 305000 - 5000
100y = 300000
y = 3000
Put value of y in equation 1
50x +100y - xy =93500
50x + 100(3000) -3000x = 93500
50x -3000x +300000 = 93500
-2950x = 93500 - 300000
-2950x = -206500
x =70
100-x = 100-70
=30
Hence the weight of gold is 30 per gm
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