Karishma
Pls see this. Lets evaluate the ratio of X : Y.
If I mix X and Y smoothie then they should yield the ratio of p:q = 24:25.
The net ratio is 24:25 or 0.96 (mean)
The ratio of X is 4:1 or 4.0
The ratio of Y is 1:5 or 0.2
Since the ratio of Y is near the weighted mean, when I combine X and Y then Y > X i.e. the quantity of Y is more than that of X -----(1)
However, I am getting X = 25 oz and Y = 24 oz by using algebra - exactly opposite of inference (1). I thought that quantity that is closer to mean will pull the mean - the quantity of Y should be more. Did I miss something?
On the other hand equations yield-
In X : p and q are in ratio 4a:a
In Y : p and q are in ratio b:5b
Now, 4a + b = 24 (total quantity of juice P)
a + 5b = 25 (total quantity of juice Q)
Solving we get a = 5, b = 4
Hence X = 5a = 5 * 5 = 25 oz
Y = 6b = 6*4 = 24 oz
or X : Y = 25 : 24
VeritasPrepKarishma wrote:
There isn't much of mixture concept you need here. It is actually based on ratios.
Smoothie X -> Juice P: 4n oz, Juice V: n oz
Juice P left for Smoothie Y: 24 - 4n
Juice V left for Smoothie Y: 25 - n
Smoothie Y ratio of P/V = \(\frac{1}{5} = \frac{(24-4n)}{(25-n)}\)
n = 5
Juice P in smoothie X = 4*5 = 20 oz