A is the average of 10 given numbers. B is the average after 2 of the numbers were replaced by 3 other different numbers. The average of the removed numbers is 48, and the average of the newly included numbers is 56. If A + B = 438, then the value of A - B is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 14.
Total of removed numbers = 2 × 48 = 96
Total of new numbers = 3 × 56 = 168
New total = 10A - 96 + 168 = 10A + 72
New count of numbers = 10 - 2 + 3 = 11
A + B = 438:
⇒ A + (10A + 72)/11 = 438
⇒ 21A = 4746
⇒ A = 226
⇒ B = 438 - A = 438 - 226 = 212
⇒ A - B = 226 - 212 = 14