Question

There are two alloys of gold, silver and platinum. the first alloy is known to contain 40 percent of platinum and the second alloy 26 percent of silver. 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 that contains 30 percent of gold. how many kilogram of platinum is there is the new alloy? (a) 170 kg (b) 175 kg (c) 160 kg (d) 165 kg (e) 180 kg

Answer 1

Hi your answer is (d) means 165 kg

Answer 2

Answer:

Total mass of platinum in the new alloy is 170 kg.

Explanation:

Mass of gold in new alloy = m

Percentage of gold in new alloy = 30%

Mass of new alloy = 150 kg + 250 kg = 400 kg

$30\%=\frac{m}{400 kg}\times 100$

m  = 120 kg

Percentage of gold in alloy-1 and alloy-2 = y%

Mass of alloy-1 = 150 kg

Percentage of platinum in alloy-1 = 40 %

Percentage of silver in alloy -1 = 100% - 40% - y%

mass of alloy -2 = 250 kg

Percentage of platinum in alloy-2 =  100% - 26% - y%

Percentage of silver in alloy -2 = 26%

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

y  = 30%

Percentage of platinum in alloy-1 = 40 %

Mass of platinum in alloy -1= $\frac{40}{100}\times 150 kg=60 kg$

Percentage of platinum in alloy-2 =  100% - 26% - y%

= 100%-26%-30%=44%

Mass of platinum in alloy-2= $\frac{44}{100}\times 250 kg=110 kg$

Total mass of platinum in new alloy = 60 kg + 110 kg = 170 kg