Read the following line graph carefully and answer the question given below.…
2024
Read the following line graph carefully and answer the question given below. The line graph shows one-third of the total items sold by five different shops in two different years.
Note:
(i). The total number of items sold by each shop in 2023 is 20% more than that in 2021.
(ii). The number of items shown in the line graph for each shop in each year is one-third of the total items sold by that shop.
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.
- A.
1:2
- B.
2:3
- C.
3:2
- D.
3:4
- E.
4:5
Show answer & explanation
Correct answer: C
Concept
In a line-graph data-interpretation problem, first translate every plotted value into the actual quantity it represents using the scaling rule in the note, then read off only the two quantities the question asks about. Here the plotted value for any shop in any year equals one-third of that shop's total items, so the true total is 3 x (plotted value). A year that is not plotted (2023) is obtained from its stated percentage relation to a plotted year (2023 = 2021 + 20%).
Key relations:
Total items of a shop in a year = 3 x (value read from the graph) for that shop-year.
Total items in 2023 = 1.20 x (Total items in 2021) for the same shop.
Application
Required ratio: total items sold by B in 2022 to total items sold by C in 2023.
From the graph, B's plotted value in 2022 = 540, so B's total in 2022 = 3 x 540 = 1620.
From the graph, C's plotted value in 2021 = 300, so C's total in 2021 = 3 x 300 = 900.
C's total in 2023 = 1.20 x 900 = 1080 (applying the 20%-increase rule to the 2021 figure).
Ratio = 1620 : 1080. Dividing both by their HCF 540 gives 1620/540 = 3 and 1080/540 = 2.
So the required ratio is 3 : 2.
Cross-check
Because the one-third factor appears in BOTH quantities, it cancels, so the ratio can also be found straight from the graph-derived figures: B(2022) plotted = 540 and C(2023) plotted = 300 x 1.20 = 360, giving 540 : 360 = 3 : 2. Both routes agree, confirming 3 : 2.