For shop B, the number of Printers and Speakers sold is ____ % more than the…
2024
For shop B, the number of Printers and Speakers sold is ____ % more than the number of cameras sold.
Answer: B. 25 — Concept The phrase "A is p% more than B" always measures the excess of A over the base B as a share of that base: p = (A − B) ÷ B × 100. The base is whichever…
- A.
40
- B.
25
- C.
10
- D.
35
Attempted by 1 students.
Show answer & explanation
Correct answer: B
Concept
The phrase "A is p% more than B" always measures the excess of A over the base B as a share of that base: p = (A − B) ÷ B × 100. The base is whichever quantity follows "more than", never the larger of the two. A second idea is needed whenever a table reports only a part of a quantity — a fixed percentage of it, a half of it — or only a ratio between two quantities: the actual count must first be recovered by inverting that percentage, that fraction, or that ratio.
Step 1 — recover the actual counts for shop B
The table never states shop B's counts directly, so each one is reconstructed from what it does state.
Item | What the data states for shop B | Actual number sold |
|---|---|---|
Cameras | 40% of the cameras sold is 320 | 320 ÷ 0.40 = 800 |
Printers | Half of the printers sold is 220 | 220 × 2 = 440 |
Speakers | Note (2): cameras : speakers = 10 : 7 | 800 × 7 ÷ 10 = 560 |
Step 2 — form the percentage comparison
Combine the two quantities being compared: printers + speakers = 440 + 560 = 1000.
Identify the base named after "more than": the camera count, 800.
Apply the concept: p = (1000 − 800) ÷ 800 × 100 = 200 ÷ 800 × 100 = 25.
Cross-check
Work the percentage forward instead of backward: 25% of 800 is 200, and 800 + 200 = 1000, which is exactly the combined printer-and-speaker count. The two routes agree, so the figure is consistent.
Where the base is easily misplaced
Dividing the same excess of 200 by the combined total of 1000 gives 20%, but that answers the reverse question — by how much the cameras fall short of the printers and speakers together — because it makes 1000 the base. The stem places the cameras after "more than", so 800 is the base.
Answer
The printers and speakers together were sold 25% more than the cameras at shop B.