In a one day cricket match of 50 overs, Team A bats first and scores at a run rate of 6.1 runs per over, so that its total is fixed. Team B is now batting. With 10 overs left to play, the required run rate for Team B to tie the match is 6.5 runs per over. What is Team B's current score at this stage?

Introduction / Context:
This question applies average rate concepts to cricket scoring. Team A has already set a target with a known run rate. Team B is partway through its innings, and you are given the required run rate for the remaining overs to tie the match. From this information, you need to determine Team B's current score.

Given Data / Assumptions:
• Total overs in the innings = 50.• Team A's run rate = 6.1 runs per over for all 50 overs.• Team B is chasing Team A's total.• There are 10 overs left for Team B, so they have already played 40 overs.• Required run rate for the remaining 10 overs to tie the match = 6.5 runs per over.• We assume no extra balls or interruptions; overs are full and complete.

Concept / Approach:
First, we calculate Team A's total runs from its run rate and overs. This total is also the target Team B must reach to tie. Then, using the required run rate and remaining overs, we compute how many runs Team B still needs. Subtracting this from the target total gives the current score of Team B.

Step-by-Step Solution:
Step 1: Team A's total runs = run rate * overs = 6.1 * 50.Step 2: Compute 6.1 * 50 = 305 runs.Step 3: To tie the match, Team B must score exactly 305 runs.Step 4: There are 10 overs left, and the required run rate is 6.5 runs per over.Step 5: Runs needed in remaining 10 overs = 6.5 * 10 = 65 runs.Step 6: Let S be Team B's current score.Step 7: To tie, S + 65 must equal 305.Step 8: So S = 305 - 65 = 240.

Verification / Alternative check:
If Team B currently has 240 runs, they need 305 - 240 = 65 more runs. With 10 overs remaining, scoring 65 runs means an exact run rate of 65 / 10 = 6.5 runs per over, which matches the required run rate stated in the question. Thus the value S = 240 is fully consistent.

Why Other Options Are Wrong:
235: This would require 70 runs in 10 overs, implying a required run rate of 7.0, not 6.5.230: This would lead to a required run rate of 7.5, again inconsistent with the given value.225: This would require 80 runs in 10 overs, an even higher required rate of 8.0 runs per over.

Common Pitfalls:
Some students incorrectly compute Team A's total or misinterpret the required run rate as the current run rate. Others might forget that the required rate applies only to the remaining overs, not to the entire innings. Carefully separating completed overs from remaining overs and applying the definitions of run rate prevents such mistakes.

Final Answer:
Team B's current score is 240 runs.