Multiple choice

A man bought a chair and sold it at a gain of $5$%. If he had bought it at $5$% less and sold it for Rs $45$ more, he would have gained $20$% . Find the cost price of the chair?

  1. Rs. $400$
  2. Rs. $500$
  3. Rs. $450$
  4. Rs. $550$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let CP be x. SP1 = 1.05x. New CP = 0.95x. New SP = 1.05x + 45. Given new gain is 20%, so 1.20 * (0.95x) = 1.05x + 45. Solving 1.14x = 1.05x + 45 gives 0.09x = 45, so x = 500.

AI explanation

Let the original cost price of the chair be Rs. x. The new cost price is 0.95x, and selling it for Rs. 45 more yields a 20% profit on this new cost, so the new selling price is 1.20 times 0.95x. The original selling price was 1.05x, giving the equation 1.05x + 45 = 1.14x. Solving this gives 0.09x = 45, so x = 500. The cost price of the chair is Rs. 500.

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