Multiple choice

A man spends Rs. $500$ in buying $12$ tables and chairs. The cost of one table is Rs.$50$ and that of one chair is $40$. What is the ratio of the numbers of the chairs and the tables purchased?

  1. $5:4$
  2. $3:2$
  3. $1:5$
  4. $5:1$
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D Correct answer
Explanation

Let c be the number of chairs and t be the number of tables. 50t + 40c = 500. Dividing by 10 gives 5t + 4c = 50. Testing integer solutions: if t=2, 10+4c=50, 4c=40, c=10. Ratio c:t = 10:2 = 5:1.

AI explanation

Let the number of tables be t and the number of chairs be c. Using the given total cost, we form the equation 50t + 40c = 500, and we also know t + c = 12. Multiplying the second equation by 50 gives 50t + 50c = 600, and subtracting the cost equation from this yields 10c = 100, so c = 10 and t = 2. The ratio of the number of chairs to the number of tables is 10:2, which simplifies to 5:1.

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