Question

An alloy of gold and silver is taken in the ratio of 1:2 and another alloy of the same metals is taken in the ratio of 2:3. How many parts of the two alloys must be taken in order to get an alloy with gold and silver in the ratio of 3:5

Answer 1

Dear Student,

◆ Answer -

3 : 5

◆ Explaination -

Let x and y be mass of two alloys mixed.

In first alloy,

Gold = x × 1 / (1 + 2) = x/3

Silver = x × 2 / (1 + 2) = 2x/3

In second alloy,

Gold = y × 2 / (2 + 3) = 2y/5

Silver = y × 3 / (2 + 3) = 3y/5

In resulting alloy, Gold / Silver = 3 / 5

(x/3+2y/5) / (2x/3+3y/5) = 3 / 5

(x/3+2y/5) × 5 = (2x/3+3y/5) × 3

5x/3 + 2y = 2x + 9y/5

5x/3 - 2x = 9y/5 - 2y

-x/3 = -y/5

x/y = 3/5

Therefore, two alloys should be taken in ratio of 3 : 5.

Thanks dear...