In cricket, the run rate is the average number of runs scored per over. In a T20 match, a team scored 6 runs in the first over making the run rate 6.
- (i) In the second over they scored 12 runs. What is the run rate now?
- (ii) After Over 19, their run rate was 6. What is the run rate after 20 overs given the team made 12 runs in the last over?
Step-by-step solution
Idea: Run rate = total runsovers bowled. A run rate after some overs tells us the total so far: runs = run rate × overs. Then add the new over’s runs and divide by the new number of overs.
(i) In the second over they scored 12 runs. What is the run rate now?
- Total runs after 2 overs = 6 + 12 = 18, so the run rate = 182 = 9.1 mark
(ii) After Over 19, their run rate was 6. What is the run rate after 20 overs given the team made 12 runs in the last over?
- Runs after 19 overs = 19 × 6 = 114. After the 20th over: 114 + 12 = 126 runs.1 mark
- Run rate = 12620 = 6.3. One big over raises the rate only a little, because it is 1 over against 19.1 mark
Check: (ii) as a weighted mean: 6 × 19 + 12 × 119 + 1 = 6.3 ✓. In (i) the two overs have equal weight, so 9 is midway between 6 and 12 ✓.
Answer to write in the exam
(i)
Runs in 2 overs = 6 + 12 = 18
Run rate = 182 = 9
∴ Run rate = 9
(ii)
Runs in 19 overs = 19 × 6 = 114
Runs in 20 overs = 114 + 12 = 126
Run rate = 12620 = 6.3
∴ Run rate after 20 overs = 6.3
Common mistakes that cost marks
- In (ii), averaging 6 and 12 to get 9. The run rate 6 stands for 19 overs, the 12 for just one.
- Dividing 126 by 19 instead of 20 overs.
- Adding 12 to the run rate (6 + 12 = 18) instead of to the total runs.
How this can come in the exam
After 10 overs a team’s run rate is 7. They score 18 runs in the 11th over. The new run rate is
- 8
- 12.5
- 7.5
- 8.8
Show answer
(A) 8
70 + 1811 = 8811 = 8.
After 15 overs a team’s run rate is 8. How many runs must it score in the next 5 overs to finish 20 overs with a run rate of 9?
Show answer
Runs needed in 20 overs = 9 × 20 = 180; runs so far = 8 × 15 = 120 (1 mark). Needed = 180 − 120 = 60 runs (1 mark).Try one yourself
After 4 overs the run rate is 5.5. In the 5th over the team scores 3 runs. Find the new run rate.
Show answer
4 × 5.5 + 35 = 255 = 5.
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