The line graph shows $\frac{1}{3}$rd of the total items sold by five different shops in two different years.

Note: (i). Total number of items sold by each shops in 2023 is 20% more than that in 2021.
(ii). The total number of items sold by each shops in each year, which is given in the line graph, is one-third of the total items sold.

Find the ratio of the total number of items sold by B in 2022 to the total number of items sold by C in 2023.

The correct option is 55 : 36.

Step-by-step Explanation:

1. Understanding the given line graph and notes:

From the image, we can observe the line graph representing 1/3rd of the total items sold by five shops (A, B, C, D, E) in two years (2021 and 2022):

Blue line represents 2021 data, and Orange line represents 2022 data.

According to Note (ii), the value shown in the graph is $\frac{1}{3}$ of the total items sold by each shop.

Therefore, Total items sold by a shop in a year = (Graph value) × 3.

2. Calculate the total items sold by B in 2022:

From the graph, for shop B in 2022 (orange line):

Graph value = 550

So, the total number of items sold by B in 2022 is:

$\text{Total items (B, 2022)}=550\times 3=1650$

3. Calculate the total items sold by C in 2023:

From Note (i), the total number of items sold by each shop in 2023 is 20% more than that in 2021.

First, find the total items sold by C in 2021 (blue line):

Graph value for C in 2021 = 300

$\text{Total items (C, 2021)}=300\times 3=900$

Now, calculate total items sold by C in 2023 (20% more than 2021):

$\text{Total items (C, 2023)}=900\times (1+\frac{20}{100})=900\times 1.2=1080$

4. Find the required ratio:

We need to find the ratio of total items sold by B in 2022 to total items sold by C in 2023:

$\text{Ratio}=\frac{1650}{1080}$

Simplifying the fraction by dividing both numerator and denominator by 30:

$\text{Ratio}=\frac{1650/30}{1080/30}$

Thus, the required ratio is 55 : 36.