cat 2021 Question 1

Question

If a certain weight of an alloy of silver and copper is mixed with 3 kg of pure silver, the resulting alloy will have 90% silver by weight. If the same weight of the initial alloy is mixed with 2 kg of another alloy which has 90% silver by weight, the resulting alloy will have 84% silver by weight. Then, the weight of the initial alloy, in kg, is

Accepted Answer

Let the alloy contain x Kg silver and y kg copper

Now when mixed with 3Kg Pure silver

we get $\frac{x+3}{x+y+3}$ = $\frac{9}{10}$

we get 10x+30 =9x+9y+27

9y-x=3 (1)

Now as per condition 2

silver in 2nd alloy = 2(0.9) =1.8

so we get $\frac{x + 1.8}{x+y+2}$ = $\frac{21}{25}$

we get 21y-4x =3 (2)

solving (1) and (2) we get y= 0.6 and x =2.4

so x+y = 3

Question 1.

Question Explanation