Nickel and iron are mixed in the ratio of 4:5 and 4:11 to make two alloys namely, X and Y, respectively. Suppose we want to make the third alloy, Z. by mixing equal quantities of X and Y. What
will be the ratio of nickel and iron present in the alloy Z?
Answers
Given,
Ratio of nickel and iron in X alloy = 4:5
Ratio of nickel and iron in Y alloy = 4:11
Z alloy is made by mixing equal quantities of both X and Y alloys.
To find,
The ratio of nickel and iron in the Z alloy.
Solution,
Let, equal quantity which is taken from X and Y are = x
[Assume x as a variable to do the further mathematical calculations.]
Nickel and iron ration in X alloy = 4:5
So, nickel from X alloy = (4/4+5) × x = 4x/9
Iron from X alloy = (5/4+5) × x = 5x/9
Nickel and iron in Y alloy = 4:11
Nickel from Y alloy = (4/4+11) × x = 4x/15
Iron from Y alloy = (11/4+11) × x = 11x/15
Total nickel in Z = 4x/9 + 4x/15 = 20x+12x/45 = 32x/45
Total iron in Z = 5x/9 + 11x/15 = 25x+33x/45 = 58x/45
Ratio = 32x/45 : 58x/45 = 32x/45 × 45/58x = 32/58 = 16:29
Hence, the ratio of nickel and iron in Z alloy is 16:29