Multiple choice

A man purchased a table and a chair for Rs $2000$. He sold the table at a profit of $20\%$ and the chair at a profit of $30\%$. His total profit was $23\%$. Find the cost price of the table.

  1. Rs $1400$
  2. Rs $600$
  3. Rs $1100$
  4. Rs $1200$
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A Correct answer
Explanation

Let the cost price of the table be x. Then 0.20x + 0.30(2000 - x) = 0.23 * 2000. Solving this gives 0.20x + 600 - 0.30x = 460, so 0.10x = 140, which means x = 1400.

AI explanation

By applying the rule of alligation, the ratio of the cost price of the table to the cost price of the chair is (30 - 23) to (23 - 20), which is 7 to 3. This means the total cost of Rs. 2000 is divided into 10 equal parts, where the table accounts for 7 parts. Seven tenths of 2000 equals Rs. 1400, making the cost price of the table Rs. 1400.

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