The average weight of 30 students is 40 kg. When the teacher's weight is included, the average rises by 1 kg. What is the teacher's weight?
71 kg. New total = 31 x 41 = 1,271 kg; old total = 30 x 40 = 1,200 kg. Teacher = 71 kg. Shortcut: 41 (the new average) + 30 x 1 (raising each student by 1) = 71.
Explain it simply
When someone joins a group and raises the average, their value must cover the new average for themselves and also lift every earlier member up to that new average. Totals are always the safest route: average x count gives total, and differences of totals give the newcomer.
Example
Question: 30 students average 40 kg. With the teacher, the average is 41 kg.
- Old total = 30 x 40 = 1,200 kg.
- New total = 31 x 41 = 1,271 kg.
- Teacher = 1,271 - 1,200 = 71 kg.
Shortcut: new average + (old count x rise) = 41 + 30 = 71.
If instead the average had dropped by 0.5 kg, the teacher would weigh 39.5 - 30 x 0.5 = 24.5 kg, which is unrealistic, so examiners usually set rises for a teacher and falls for a small child joining.
console.log(31 * 41 - 30 * 40); // Output: 71What to say in the interview
"I work with totals: 31 times 41 minus 30 times 40 is 71 kilos. The quick version is the new average plus one extra kilo for each of the 30 students."
Common mistakes
- Answering 41 kg, the new average.
- Multiplying the rise by 31 instead of 30.