Multiple choice

Directions: Study the following information carefully and answer the question. Three persons A, B and C altogether have a sum of Rs. 7200. If A gives B the same amount of money that B already has and B gives C the same amount of money that C already has, then all of them have equal amount of money. What is the ratio of the amounts that A, B and C respectively have initially?

  1. 12 : 8 : 3

  2. 7 : 3 : 2

  3. 13 : 12 : 11

  4. 4 : 2 : 1

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let initial amounts be A, B, C. After transfers, each has 7200/3 = 2400. Working backwards: before C gave to B, C had 2400/2 = 1200. B had 2400 + 1200 = 3600, so before B gave to C, B had 3600/2 = 1800. A had 2400 + 1800 = 4200. Ratio 4200:1800:1200 simplifies to 7:3:2.

AI explanation

Since all three persons end up with equal amounts, they must each have 2400 rupees after the transactions. Working backwards from the final state, before B gave C the same amount C had, C had 1200 rupees and B had 3600 rupees, while A was already at 2400 rupees. Before A gave B the same amount B had initially, B had 1800 rupees, A had 4200 rupees, and C maintained 1200 rupees. Dividing their initial amounts of 4200, 1800 and 1200 rupees by their highest common factor of 600 gives the ratio of 7 to 3 to 2.

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