A factory makes x chairs and y tables in a day. Match each condition in List-I with its constraint in List-II.
| List-I | List-II | ||
|---|---|---|---|
| Condition | Constraint | ||
| (A) | The number of tables is at least twice the number of chairs. | (I) | \(x \le 2y\) |
| (B) | The number of tables exceeds the number of chairs by at most 3. | (II) | \(y - x \le 3\) |
| (C) | At least 30 pieces of furniture are made in all. | (III) | \(y \ge 2x\) |
| (D) | The number of chairs is at most twice the number of tables. | (IV) | \(x + y \ge 30\) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A)-(III), (B)-(II), (C)-(IV), (D)-(I)
“At least” gives \(\ge\) and “at most” gives \(\le\). The key is to see which quantity is compared with which.
(A) The number of tables is at least twice the number of chairs.
This matches (III). Tables = y and twice the chairs = 2x, so
\(y \ge 2x\)
(B) The number of tables exceeds the number of chairs by at most 3.
This matches (II). The excess of tables over chairs is y − x, and it is at most 3:
\(y - x \le 3\)
(C) At least 30 pieces of furniture are made in all.
This matches (IV). The total made is x + y:
\(x + y \ge 30\)
(D) The number of chairs is at most twice the number of tables.
This matches (I). Chairs = x and twice the tables = 2y:
\(x \le 2y\)