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In 3500gm rod 74% is silver = 2590gm
500gm rod is added total weight becomes 4000gm
In 4000gm 84% is silver =3360gm
diff in silver =770gm
So by adding 500gm of rod 770gm of silver is increased,
which is not possible.
The percentage of silver in 0.5 kg rod is 10.5%.
In 3500 g rod contains 74% of silver = 3500 * 74/100 = 2590 g
Then 3500 g + 500 g of rod contains 84% of silver
Let x be the silver contained in 500 g of silver
(2590/3500 * 100) + (x/500 * 100) = 84
74 + x/5 = 84
(370 + x) /5 = 84
370 + x = 420
x = 50
Then the percentage of silver contained in 500 g of rod = 50/500 *100 =10%