Question

A and B are alloys of silver and copper. An alloy that is 5 parts A and 3 parts B is 52% silver. One that is 5 parts A and 11 parts B is 42% silver. What are the percentages of silver in A and B, respectively?

Answer 1

Let there be x% of silver in A and y% of silver in B.

Then by the given conditions we have,

(5x+3y)/(5+3) = 52

i.e., 5x+3y = 416........(i)

And, (5x+11y)/(5+11) = 42

i.e., 5x+11y = 672..........(ii)

Subtracting (i) from (ii) we get,

8y = 256

i.e., y = 256/8

i.e., y = 32

Putting this value in (i) we get,

5x+(3×32) = 416

i.e., 5x+96 = 416

i.e., 5x = 416-96

i.e., 5x = 320

i.e., x = 320/5

i.e., x = 64

Therefore, there are 64% of silver in A and 32% of silver in B.