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 difference between the total number of items sold by D and E together in 2023 and the total number of items sold by A and B together in 2021.

The correct answer is 180.

Step-by-Step Explanation:

1. Understanding the given data from the line graph and notes:

The line graph shows $\frac{1}{3}$rd of the total items sold by five shops (A, B, C, D, and E) in the years 2021 and 2022.

From note (ii), the graph values represent $\frac{1}{3}$rd of the total items sold in that respective year.

From the line graph for the year 2021 (represented by the blue line):
• $\frac{1}{3}$rd of items sold by shop A in 2021 = 600
⇒ Total items sold by shop A in 2021 = 600 × 3 = 1800

• $\frac{1}{3}$rd of items sold by shop B in 2021 = 420
⇒ Total items sold by shop B in 2021 = 420 × 3 = 1260

• $\frac{1}{3}$rd of items sold by shop D in 2021 = 520
⇒ Total items sold by shop D in 2021 = 520 × 3 = 1560

• $\frac{1}{3}$rd of items sold by shop E in 2021 = 280
⇒ Total items sold by shop E in 2021 = 280 × 3 = 840

2. Calculate the total number of items sold by A and B together in 2021:

Total items sold by A and B in 2021 = 1800 + 1260 = 3060

3. Calculate the total number of items sold by D and E together in 2023:

From note (i), the total number of items sold by each shop in 2023 is 20% more than that in 2021.
This means for any shop, Total items in 2023 = Total items in 2021 × (1 + 0.20) = Total items in 2021 × 1.2.

• Total items sold by shop D in 2023 = 1560 × 1.2 = 1872
• Total items sold by shop E in 2023 = 840 × 1.2 = 1008

Total items sold by D and E together in 2023 = 1872 + 1008 = 2880

4. Find the required difference:

Difference = (Total items sold by A and B together in 2021) - (Total items sold by D and E together in 2023)

Difference = 3060 - 2880 = 180

Hence, the required difference is 180.