If the ratio of the number of items sold by B and C together on Thursday to…
2024
If the ratio of the number of items sold by B and C together on Thursday to the number of items sold by C and E together on the same day is 2 : 1, then the number of items sold by C on Thursday is:
Answer: C. 380 — Concept: A ratio statement is an equation, not a description. If two quantities satisfy P : Q = m : n, then cross-multiplication gives n × P = m × Q. When the…
- A.
300
- B.
420
- C.
380
- D.
340
Show answer & explanation
Correct answer: C
Concept: A ratio statement is an equation, not a description. If two quantities satisfy P : Q = m : n, then cross-multiplication gives n × P = m × Q. When the same unknown sits inside both P and Q, that cross-multiplication collapses to a single linear equation in one unknown, which is then solved by ordinary transposition.
Application: Only the Thursday row of the table is involved. It reads:
Day | A | B | C | D | E |
|---|---|---|---|---|---|
Thursday | 1080 | 1020 | x (missing) | 1260 | 320 |
Let the number of items sold by C on Thursday be x.
Form the two aggregates named in the question: B and C together = 1020 + x, and C and E together = x + 320.
Write the given condition as an equation: (1020 + x) : (x + 320) = 2 : 1.
Cross-multiply: 1 × (1020 + x) = 2 × (x + 320).
Expand the right side: 1020 + x = 2x + 640.
Transpose like terms: 1020 − 640 = 2x − x.
Simplify: x = 380. So C sold 380 items on Thursday.
Cross-check: Substituting x = 380 gives B and C together = 1020 + 380 = 1400, and C and E together = 380 + 320 = 700. Since 1400 : 700 = 2 : 1, the stated condition is satisfied exactly.
Note: The blank entries in the Monday, Tuesday, Wednesday and Friday rows are irrelevant to this question — a ratio condition confined to a single day is solved from that day’s row alone.