What is the ratio of the number of speakers sold by shop B to the number of…
2024
What is the ratio of the number of speakers sold by shop B to the number of speakers sold by shop D?
Answer: C. 4:5 — Concept: If p% of a quantity equals v, the full quantity is v × 100/p. If two quantities are in the ratio a:b, the second quantity equals the first quantity ×…
- A.
9:2
- B.
7:8
- C.
4:5
- D.
3:2
Show answer & explanation
Correct answer: C
Concept: If p% of a quantity equals v, the full quantity is v × 100/p. If two quantities are in the ratio a:b, the second quantity equals the first quantity × b/a.
To compare two derived quantities, calculate both in the same unit and reduce their ratio by dividing both terms by their greatest common divisor.
Application
For shop B, 40% of the cameras sold is 320, so the number of cameras sold is 320 × 100/40 = 800.
For shop B, cameras:speakers = 10:7, so the number of speakers sold is 800 × 7/10 = 560.
For shop D, 40% of the cameras sold is 240, so the number of cameras sold is 240 × 100/40 = 600.
For shop D, cameras:speakers = 6:7, so the number of speakers sold is 600 × 7/6 = 700.
Therefore, the required ratio is 560:700. Dividing both terms by 140 gives 4:5.
Cross-check
The fraction 560/700 equals 0.8, and 4/5 also equals 0.8, confirming the reduction.
Result: The ratio of speakers sold by shop B to those sold by shop D is 4:5.