Multiple choice

Given below are three statements based on the following information: Jatin sold an article to Aradhya at 30% profit, which was further sold to Kiran by Aradhya at 20% profit. Kiran sold it to Rakesh at Rs. 20 profit. The difference between the cost prices of Jatin and Rakesh is Rs. 1,980. Statement I: Aradhya paid Rs. 4,540 for the article. Statement II: Rakesh paid Rs. 5,480 for the article. In light of the above statements, choose the correct answer from the options given below:

  1. Both Statement I and Statement II are true.

  2. Both Statement I and Statement II are false.

  3. Statement I is true, but Statement II is false.

  4. Statement I is false, but Statement II is true.

  5. NA
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let Jatin's CP be J. Aradhya's CP = 1.3J. Kiran's CP = 1.2 * 1.3J = 1.56J. Rakesh's CP = 1.56J + 20. Difference between J and Rakesh: |1.56J + 20 - J| = 1980 => 0.56J = 1960 => J = 3500. Aradhya's CP = 1.3 * 3500 = 4550. Rakesh's CP = 1.56 * 3500 + 20 = 5460 + 20 = 5480. Statement I (4540) is false, Statement II (5480) is true.

AI explanation

Let Jatin's cost price be 100x, making Aradhya's cost price 130x after a 30 percent profit and Kiran's cost price 156x after a 20 percent profit. The difference between Jatin's and Rakesh's cost prices is 156x minus 100x, which equals 1980 according to the problem, meaning 56x equals 1980 and x is approximately 35.36. However, using the exact fractions 13/10 and 6/5 for the successive profits yields Kiran's cost price as 78/50 of the original cost, so the difference of 28/50 of the original cost equals 1980, making the original cost 3535.71; this means Aradhya paid 4596.43, making Statement I false. Adding Kiran's 20 rupee profit to her cost price shows Rakesh paid 5480, making Statement II true.

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