Question
The average of 20 numbers is 75. The average of the
first 12 numbers is 80, while the average of the last 11 numbers is 68. If the 12th number is removed, what will be the average of the remaining 19 numbers?Solution
ATQ, Sum of 20 numbers = 75 × 20 ⇒ 1500 Sum of first 12 numbers = 80 × 12 ⇒ 960 Sum of last 11 numbers = 11 × 68 ⇒ 748 Let the 12th number be x Sum of 20 numbers = Sum of first 12 numbers + Sum of last 11 numbers - 12th number ⇒ 1500 = 960 + 748 - x ⇒ 1500 = 1708 - x ⇒ x = 1708 - 1500 ⇒ x = 208 Sum of remaining numbers = 1500 - 208 ⇒ 1292 Remaining numbers = 19 Average of remaining numbers = 1292 / 19 ⇒ 68
10                          15                          ?                    �...
If   314     306      x      269       394    178    1480
Then, 1/3 x + 2x - x = ?
...12Â Â Â Â Â 13Â Â Â Â Â Â 22Â Â Â Â Â Â 47Â Â Â Â Â 96Â Â Â Â Â ?
...24  12  18  ?  157.5  708.75  3,898.125
21Â Â Â Â Â Â Â Â Â Â 48Â Â Â Â Â Â Â Â Â Â 173Â Â Â Â Â Â Â Â 516Â Â Â Â Â Â Â Â 1245Â Â Â Â Â Â 2576Â Â Â Â Â Â ?
...51     53     109     332     ?     6686
...9 134 170 ? 577 1306
...12    16    43    ?       184    220
...13 24 75 134 447 892
...97 106 121 138 157 180
...
