Hi,
Let n be the total stock
red = n/6
blue = (1/4)*(n - n/6) = 5n/24
Given m = 5n/24
So, n/6 = 4m/5

Hence, D

Answer is D.
Red sold = 1/6
Out of remaining: 1-1/6 = 5/6, 1/4 sold was blue = 5/24.
Answered asked is if number of blue sold is m then, what is red in terms of m.
Let total number of piesces be 48(we should take a number divisible by 6 and 24 and which can give us answers not in fractions.
So the number of red sold = 48/6 = 8.
The number of blue sold = 48-8/4= 10.
so red in term of blue = 8/10 = 4/5.
Hence, D

Is the question asking Red sold, or red available at the stock at the very beginning?

@ Frankenstine:Salute sir
I didn't know how to go about with 5/24, so resorted to plug ins, but you made it look so easy!
Great, dude!

how much red was sold.

Let me post the solution. Frankestein's solution seems great!

Here it is:

We are told that some of the stock at a shop is blue, some is red, and some must be other colors. We are asked to find how much of the stock that the store sold was red, in terms of m, the amount of blue stock sold.

The red stock was 1/6 of the store's total stock, which means that 5/6 of the stock was not red. We know that m is equal to one quarter of the stock that was not red, which means that m is 1/4 of 5/6 of the store's total stock, or 5/24 of the total stock.

The ratio of red stock to blue stock is constant, so we can use the fractions we already know to represent both the fraction of the stock that is red 1/6 and the fraction that is blue 5/24, and put them into a ratio equivalent to the ratio of red to blue generally: (1/6)/(5/24) = R/m.

Since dividing by a fraction is the same as multiplying by its reciprocal, we can simplify the left-hand side of the equation by multiplying by 24/5 to get 4/5.

Now we have (4/5)=R/m.

I know how he got it!

(4/5)m