Read the following information carefully and answer the questions given below. The information about three sellers who sold two types of rice, i.e., brown and white.

The quantity of white rice sold by all three seller is 230 kg. The quantity of brown rice sold by B is 20% more than the quantity of white rice sold by A. The quantity of white rice sold by B is 20 kg more than that of brown rice. The ratio of brown rice sold by A to B is 2:3. The average quantity of brown rice sold by all three sellers is 60 kg, and the total rice (white and brown) sold by C is 75 kg.

Find the ratio of the total quantity of white rice sold by B to the total quantity of brown rice sold by A and B together.

To find the ratio of the quantity of white rice sold by B to the total quantity of brown rice sold by A and B together, we need to determine the individual quantities for each seller step-by-step.

Let the quantities of white rice sold by A, B, and C be represented by $W_A$, $W_B$, and $W_C$ respectively.
Similarly, let the quantities of brown rice sold by A, B, and C be represented by $B_A$, $B_B$, and $B_C$ respectively.

From the given information, we can set up the following relationships:

1. Total white rice sold by all three sellers:
$W_A+W_B+W_C=230$ (Equation 1)

2. Brown rice sold by B:
The quantity of brown rice sold by B is 20% more than the white rice sold by A:
$B_B=1.2\times W_A$ (Equation 2)

3. White rice sold by B:
The quantity of white rice sold by B is 20 kg more than B's brown rice:
$W_B=B_B+20=1.2\times W_A+20$ (Equation 3)

4. Brown rice sold by A:
The ratio of brown rice sold by A to B is 2:3:
$\frac{B_A}{B_B}=\frac{2}{3}\Rightarrow B_A=\frac{2}{3}{B}_B=\frac{2}{3}(1.2\times W_A)=0.8\times W_A$ (Equation 4)

5. Total brown rice sold by all three sellers:
The average quantity of brown rice sold by all three sellers is 60 kg:
$B_A+B_B+B_C=3\times 60=180$ (Equation 5)

6. Total rice sold by C:
The total quantity of rice (white and brown) sold by C is 75 kg:
$W_C+B_C=75\Rightarrow W_C=75-B_C$ (Equation 6)

Now, substitute the expressions for $W_B$ and $W_C$ into Equation 1:
$W_A+(1.2\times W_A+20)+(75-B_C)=230$
$2.2\times W_A+95-B_C=230$
$B_C=2.2\times W_A-135$ (Equation 7)

Next, substitute $B_A$, $B_B$, and $B_C$ in terms of $W_A$ into Equation 5:
$0.8\times W_A+1.2\times W_A+(2.2\times W_A-135)=180$
$4.2\times W_A-135=180$
$4.2\times W_A=315$
$W_A=\frac{315}{4.2}=75\text{kg}$

Using $W_A=75$ kg, we calculate the remaining values:
$B_B=1.2\times 75=90\text{kg}$
$W_B=90+20=110\text{kg}$
$B_A=0.8\times 75=60\text{kg}$

Now, let's find the required ratio:
- Total quantity of white rice sold by B = $W_B=110\text{kg}$
- Total quantity of brown rice sold by A and B together = $B_A+B_B=60+90=150\text{kg}$

The required ratio is:
$\text{Ratio}=\frac{110}{150}=\frac{11}{15}$

Therefore, the correct option is 11:15.