Question

There are two alloys of copper and zinc. In the first allo
y, there is twice as much copper as zinc, and in the sec
ond alloy there is 5 times less copper than zinc. How
many times more must we take of the second alloy tha
n the first in order to obtain a new alloy in which there
would be twice as much zinc as copper?​

Answer 1

Answer:

many times more must we take of the second alloy tha

n the first in order to obtain a new alloy in which there

would be twice as much zinc as copper

Answer 2

Given:

The ratio of copper to zinc in the 1st alloy = 2 : 1

The ratio of copper to zinc in the 2nd alloy = 1 : 5

To Find:

The ratio of the two alloys needed to obtain a new alloy in which there  would be twice as much zinc as copper.

Solution:

The resultant alloy has copper and zinc in the ratio 1 : 2

Let 'a' parts of alloy 1 and 'b' parts of alloy 2 be mixed to obtain the resultant alloy.

Therefore, the amount of copper in the resultant alloy will be = Amount of Cu from a parts of alloy 1 + Amount of Cu from b parts of alloy 2

= $\frac{2}{3} a + \frac{1}{6} b = \frac{1}{3}$        - (1)

Similarly, the amount of zinc in the resultant alloy will be

= $\frac{1}{3} a + \frac{5}{6} b = \frac{2}{3}$         - (2)

Solving equations (1) and (2) using the elimination method, we get:

a = 0.33

and b = 0.66

Thus, alloy 1 and alloy 2 should be used in the ratio 1 : 2.