Question

There are two alloys of platinum, silver and gold. The first alloy is known to contain $40$ per cent of platinum and the silver alloy $26$ per cent of copper. The percentage of gold is the same in both alloys. Having alloyed $150$ kg of the first alloy and $250$ kg of the second, we get a new alloy which contains $30$ per cent of gold. How many kg of platinum are there in the new alloy?

Answer 1

FIRST ALLOY

$1^{st}$ Alloy $150kg$ is used.

$40$% is platinum in first alloy

$\frac{40}{100}\times 150=60kg$ of PLATINUM

SECOND ALLOY

$2^{nd}$ ALLOY $250kg$ is used

$26$% of silver $=\frac{26}{100}\times 250=65kg$

New alloy $=150+250=400kg$ has $30$% gold $=\frac{30}{100}\times 400=120kg$ gold

since both contain same % of gold $x$% of $150$ $+$ $x$% of $250=120$

$\frac{x}{100}\times 150+\frac{x}{100}\times 250=120$

$1.5x+2.5x=120$

$x=30$%

In second alloy $100-(30+26)=44$% of platinum is there

$44$% of $250$ $=\frac{44}{100}\times 250=110kg$

In new Alloy Platinum is $110+60kg$ $=170kg$