Multiple choice

The average of two numbers increases by 20 when one of the numbers is doubled and it increases by 25 when the other number is doubled. What is the average of both numbers?

  1. 40

  2. 45

  3. 50

  4. Cannot be determined

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

Let the numbers be x and y. Average = (x+y)/2. If x is doubled: (2x+y)/2 - (x+y)/2 = 20 => x/2 = 20 => x = 40. If y is doubled: (x+2y)/2 - (x+y)/2 = 25 => y/2 = 25 => y = 50. Average = (40+50)/2 = 45.

AI explanation

Let the sum of the two numbers be S, so their original average is S divided by 2. When the first number is doubled, the increase in the sum is the first number, which increases the average by 20, meaning the first number is 2 times 20, or 40. Similarly, the second number is 2 times 25, or 50. Adding 40 and 50 gives a sum of 90, and dividing by 2 gives an average of 45. The average of both numbers is 45.

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