A shop stocks x chairs and y tables. Match each condition in List-I with the inequality that expresses it in List-II.
| List-I | List-II | ||
|---|---|---|---|
| Condition | Inequality | ||
| (A) | The number of chairs is at least twice the number of tables | (I) | \(x + 4y \le 40\) |
| (B) | The chairs and tables together number at most 20 | (II) | \(x - y \ge 4\) |
| (C) | A chair costs Rs. 500, a table costs Rs. 2000, and at most Rs. 20000 can be spent | (III) | \(x - 2y \ge 0\) |
| (D) | The number of chairs is more than the number of tables by at least 4 | (IV) | \(x + y \le 20\) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
(A) “At least twice” gives \(x \ge 2y\), that is, \(x - 2y \ge 0\) — (III).
(B) “At most 20 in all” gives \(x + y \le 20\) — (IV).
(C) The cost is \(500x + 2000y \le 20000\); dividing by 500 gives \(x + 4y \le 40\) — (I).
(D) “More by at least 4” gives \(x \ge y + 4\), that is, \(x - y \ge 4\) — (II).