In an alloy, zinc and copper are in the ratio 1:3. In the second alloy the same elements are in the ratio 2:3. If what proportion should the two alloys be mixed so as to form a new alloy in which zinc and copper are in the ratio 1:2.

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Solution

Let the required ratio of first to second type be $1 : x$
According to question $\frac{1 \times \frac{1}{4} + x \times \frac{2}{5}}{1 \times \frac{3}{4} + x \times \frac{3}{5}} = \frac{1}{2}$
On solving we get $x = \frac{5}{4}$
So required ratio of first to second type = $4 : 5$

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In an alloy, zinc and copper are in the ratio 1:3. In the second alloy the same elements are in the ratio 2:3. If what proportion should the two alloys be mixed so as to form a new alloy in which zinc and copper are in the ratio 1:2.

Let the required ratio of first to second type be 1:xAccording to question 1×14+x×251×34+x×35=12On solving we get x=54So required ratio of first to second type = 4:5

Let the required ratio of first to second type be $1 : x$
According to question $\frac{1 \times \frac{1}{4} + x \times \frac{2}{5}}{1 \times \frac{3}{4} + x \times \frac{3}{5}} = \frac{1}{2}$
On solving we get $x = \frac{5}{4}$
So required ratio of first to second type = $4 : 5$