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 1/3rd of the total items sold by five different shops in two different years.
Note:
The total number of items sold by each shop in 2023 is 20% more than that in 2021.
The number shown in the line graph for each shop in each year is one-third of the total items sold by that shop in that year.
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.
Answer: A. 180 — Concept: When a chart shows a fixed fraction of a quantity, recover the actual quantity by multiplying the charted value by the reciprocal of that fraction.…
- A.
180
- B.
194
- C.
150
- D.
160
- E.
100
Attempted by 5 students.
Show answer & explanation
Correct answer: A
Concept: When a chart shows a fixed fraction of a quantity, recover the actual quantity by multiplying the charted value by the reciprocal of that fraction. Here every plotted point is one-third of the items sold, so actual items sold = 3 × (plotted value). A 20% increase means multiplying by 1.20 (i.e. value + value/5).
Application:
Recover actual items from the 2021 line (plotted value is one-third, so multiply by 3): A in 2021 = 3 × 600 = 1800; B in 2021 = 3 × 420 = 1260; D in 2021 = 3 × 520 = 1560; E in 2021 = 3 × 280 = 840.
A and B together in 2021 = 1800 + 1260 = 3060.
D and E together in 2021 = 1560 + 840 = 2400. By Note (i), 2023 is 20% more than 2021, so D and E together in 2023 = 2400 × 1.20 = 2880.
Required difference = 3060 - 2880 = 180.
Cross-check: work in plotted units first. A+B plotted = 600+420 = 1020; D+E plotted = 520+280 = 800, raised 20% = 960. Difference in plotted units = 1020 - 960 = 60, and the actual difference = 3 × 60 = 180, which agrees.