A batsman scores 85 runs in his 17th innings and his average goes up by 3. What is his average after the 17th innings?
37. If the old average was a, then 16a + 85 = 17(a + 3), so a = 34 and the new average is 37. Quick view: 85 covers the new average once plus 3 extra for each of the 16 earlier innings, so new average = 85 - 16 x 3 = 37.
Explain it simply
The 85 runs do two jobs. They lift each of the 16 earlier innings by 3 runs (48 runs in total), and what remains is the new average for the 17th innings itself. So subtract the "lifting" cost from the new score. This idea works for every "average increases when one more value is added" problem.
Example
Question: After 16 innings the average is a. He scores 85 in the 17th, and the average rises by 3.
Method 1, equation:
- Total after 16 innings = 16a.
- Total after 17 innings = 16a + 85 = 17(a + 3) = 17a + 51.
- a = 85 - 51 = 34. New average = 37.
Method 2, shortcut: New average = 85 - 16 x 3 = 85 - 48 = 37.
Check: 16 x 34 = 544, plus 85 = 629, and 629 / 17 = 37.
const oldAvg = 34;
console.log((16 * oldAvg + 85) / 17); // Output: 37What to say in the interview
"The 85 runs raise each of the 16 earlier innings by 3, which uses 48 runs. The remaining 37 is the new average. The equation 16a plus 85 equals 17 times a plus 3 gives the same answer."
Common mistakes
- Giving the old average (34) when the question asks for the new one.
- Multiplying the rise by 17 instead of 16 in the shortcut.