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.

The total quantity of white rice sold by B is what percentage of the total quantity of brown rice sold by A?

The correct answer is 183.33%.

Step-by-step Explanation:

Let us denote the quantity of white rice sold by sellers A, B, and C as $W_A$, $W_B$, and $W_C$ respectively. Similarly, let the quantity of brown rice sold by them be $B_A$, $B_B$, and $B_C$ respectively.

Based on the information given in the question, we can set up the following relationships:

1. The total quantity of white rice sold by all three sellers is 230 kg:
$W_A+W_B+W_C=230$

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

3. The quantity of white rice sold by B is 20 kg more than that of brown rice sold by B:
$W_B=B_B+20=1.2\times W_A+20$

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

5. The average quantity of brown rice sold by all three sellers is 60 kg:
$\frac{B_A+B_B+B_C}{3}=60\Rightarrow B_A+B_B+B_C=180$
Substituting the expressions in terms of $W_A$:
$0.8\times W_A+1.2\times W_A+B_C=180$
$2\times W_A+B_C=180\Rightarrow B_C=180-2\times W_A$

6. The total rice (white and brown) sold by C is 75 kg:
$W_C+B_C=75$

Now, let us substitute $W_B$ into the first equation:
$W_A+(1.2\times W_A+20)+W_C=230$
$2.2\times W_A+W_C=210\Rightarrow W_C=210-2.2\times W_A$

Substituting the expressions for $W_C$ and $B_C$ in terms of $W_A$ into the total sold by C:
$(210-2.2\times W_A)+(180-2\times W_A)=75$
$390-4.2\times W_A=75$
$4.2\times W_A=390-75$
$4.2\times W_A=315$
$W_A=\frac{315}{4.2}=75\text{kg}$

With $W_A=75\text{kg}$, we can find the required values:
• Total quantity of white rice sold by B:
$W_B=1.2\times 75+20=90+20=110\text{kg}$
• Total quantity of brown rice sold by A:
$B_A=0.8\times 75=60\text{kg}$

Now, calculate the percentage:
$\text{Percentage}=\frac{W_B}{B_A}\times 100\%=\frac{110}{60}\times 100\%=\frac{11}{6}\times 100\%\approx 183.33\%$