Question

In the first 10 overs of a cricket game, the run rate was only \(3.2\). What should be the run rate in the remaining 40 overs to reach the target of \(282\) runs?

• A. \(6.25\)
• B. \(6.5\)
• C. \(6.75\)
• D. \(7\)

Hint:

In run-rate problems, always: (i) compute runs already scored, (ii) subtract from target to get remaining runs, and (iii) divide by overs left.
A quick accuracy check is to multiply the required rate by remaining overs and add the runs already scored to confirm the target.

Answer 1

The Correct Option is A

Step 1 (Translate given information).
First \(10\) overs run rate \(= 3.2\) runs/over overs played \(= 10\).
Total target \(= 282\) runs.
Total overs in the innings \(= 50\) overs remaining \(= 50 - 10 = 40\).
Step 2 (Runs already scored in the first 10 overs).
Runs scored \(= \text{run rate} \times \text{overs} = 3.2 \times 10 = 32\).
Step 3 (Runs still required).
Runs required \(= \text{target} - \text{runs scored} = 282 - 32 = 250\).
Step 4 (Compute the required run rate for the remaining overs).
Required run rate \(= \dfrac{\text{runs required}}{\text{overs remaining}} = \dfrac{250}{40}\).
Simplify: \(\dfrac{250}{40} = \dfrac{25}{4} = 6.25\) runs per over.
Step 5 (Verification to avoid slip-ups).
If the team scores at \(6.25\) for \(40\) overs runs \(= 6.25 \times 40 = 250\).
Add the earlier \(32\) runs \(250 + 32 = 282\) target exactly met.
Step 6 (Conclude and map to option).
Therefore, the required run rate is \(6.25\) runs/over, which is Option 1.
\[ \boxed{6.25 \ \text{runs per over (Option (a)}} \]