Multiple choice

P, Q and R have 50, a and b coins with them, respectively. If Q gives 15 coins to R, he is left with 1 3 the number of coins R has now. If together they had 50 more coins, the average number of all coins would have been 100. What is the value of a : b?

  1. 2 : 5

  2. 13 : 27

  3. 1 : 2

  4. 1 : 3

  5. 49 : 110
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

P=50, Q=a, R=b. Q gives 15 to R: R becomes b+15, Q becomes a-15. (a-15) = 1/3 * (b+15) => 3a - 45 = b + 15 => 3a - b = 60. Together they had 50 more coins: (50+a+b+50)/3 = 100 => 100+a+b = 300 => a+b = 200. Solving: 4a = 260 => a = 65. b = 135. a:b = 65:135 = 13:27.

AI explanation

Let the initial number of coins with Q and R be a and b. Using the average formula, if the total coins increase by 50 to reach an average of 100 for 3 people, the new total is 300, making the original total 250; therefore, 50 + a + b = 250, which gives a + b = 200. After Q gives 15 coins to R, Q has a - 15 coins and R has b + 15 coins, and the problem states a - 15 = (1/3)(b + 15), so 3a - 45 = b + 15 and 3a - b = 60. Solving the system of equations by substituting b = 200 - a into the second equation gives 3a - (200 - a) = 60, resulting in 4a = 260 and a = 65; therefore, b = 135, making the ratio a : b equal to 65 : 135, which simplifies to 13 : 27.

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