How to Solve Average Runs and Batting Average Problems
Solve average runs and batting average aptitude problems using total-runs equations and the not-out rule, with a worked example and practice.
Expected Interview Answer
Average runs problems — commonly framed as a batting average that must rise or fall by a stated amount after the next innings — are solved by converting the current average to a total runs figure, adding the unknown next-innings score as a variable, and setting the new total divided by the new innings count equal to the target average.
If a player has scored a total of T runs in n innings (T = current average × n), and the next innings score is the unknown x, the new average condition becomes (T + x) ÷ (n + 1) = new target average, which is one linear equation solvable directly for x. When “not out” innings are involved, batting average uses completed dismissals rather than innings played in the denominator, which changes the count used — a frequently tested distinction. The same total-runs framework extends to “average runs needed over the remaining innings of a series” by treating the required total as target average × total innings, then subtracting runs already scored.
- One linear equation isolates the unknown next-innings score directly
- Generalizes to any “average must reach X” target-setting problem
- Highlights the not-out distinction, a classic exam trap
AI Mentor Explanation
This is the direct case: a batter’s average is total runs divided by dismissals, and asking what score in the next innings raises the average to a target value is solved by setting (current total + x) divided by (dismissals + 1) equal to that target and solving for x. The subtlety examiners test is that a not-out innings does not add to the dismissal count in the denominator, only to the innings count, so batting average and “runs per innings” can diverge.
Worked example (batting average target)
Current total
- 800 runs, 20 innings
- Average = 40
Target equation
- (800 + x) / 21 = 42
Required score
- x = 882 − 800 = 82
Step-by-Step Explanation
Step 1
Convert current average to total
Total = Current average × innings played (or dismissals, if not-outs matter).
Step 2
Set up the target equation
(Current total + x) ÷ (innings + 1) = target average.
Step 3
Solve for x
Isolate x: x = target average × (innings + 1) − current total.
Step 4
Check the not-out rule
If the next innings is not out, the denominator for the new average may not increase.
What Interviewer Expects
- Correct total-runs conversion from the current average
- Correct linear equation setup for the target average
- Awareness that “not out” innings change the dismissal count, not just the innings count
- Ability to solve the same structure for “runs needed over remaining innings” variants
Common Mistakes
- Using innings played instead of dismissals when not-outs are involved
- Forgetting to increase the denominator by 1 for the new innings
- Solving for the wrong unknown (target average vs required score)
- Sign errors when the average must decrease rather than increase
Best Answer (HR Friendly)
“I convert the current average into a total by multiplying by innings played, then set up one equation: the new total, divided by the new innings count, equals the target average, and solve for the unknown next score. The one trap to watch is the not-out rule — batting average divides by dismissals, not innings, so a not-out innings changes the denominator differently than a completed one.”
Follow-up Questions
- How does a not-out innings change the batting average calculation?
- How would you find the runs needed across the remaining matches of a series to hit a target series average?
- What if the target is to keep the average unchanged rather than raise it?
- How would you find the average after removing one poor innings from the record?
MCQ Practice
1. A batter has 900 runs in 18 innings (no not-outs). To raise the average to 55 after the next innings, they must score?
(900+x)/19 = 55 → 900+x = 1045 → x = 145.
2. A player’s average runs per match is 35 over 10 matches. After the 11th match their average drops to 33. Runs scored in the 11th match?
Old total = 350; new total = 33×11 = 363; 11th match runs = 363−350 = 13.
3. A batter’s batting average uses which denominator?
Batting average is total runs divided by the number of times dismissed, not innings played.
Flash Cards
Batting average formula? — Total runs ÷ number of dismissals (not simply innings played).
Equation for a target next-innings score? — (Current total + x) ÷ (innings + 1) = target average, solve for x.
Effect of a not-out innings? — Adds to innings played but not to the dismissal count used in the average.
How to find required average runs over remaining matches? — Target total (target average × total matches) minus runs already scored, over matches remaining.