On a certain date, Pakistan has a success rate of 60% against India in all the One Day International matches played between the two countries.\nPakistan then loses the next 30 ODIs in a row to India, after which its overall success rate falls to 30%.\nWhat is the total number of ODIs played between the two countries after these 30 consecutive losses?

Introduction / Context:
This problem applies percentage concepts to sports statistics. Pakistan has an initial success rate expressed as a percentage, meaning the proportion of matches won out of those played. After losing several matches in a row, the success rate changes. We need to use this information to determine the total number of matches played. Questions of this type are common in quantitative reasoning, where success rates and changes in performance over time must be modelled algebraically.

Given Data / Assumptions:

• Initially, Pakistan success rate against India in ODIs is 60%.
• Pakistan then loses the next 30 ODIs consecutively.
• After these 30 losses, the overall success rate falls to 30%.
• We assume only wins and losses, with no ties or abandoned matches affecting the statistics.
• We must find the total number of ODIs played between the two countries after these 30 losses.

Concept / Approach:
Let the initial number of matches played be N, with Pakistan winning 60% of them. That means the number of wins is 0.60 * N. The team then plays 30 more matches and loses all of them, so the number of wins remains the same while the total number of matches becomes N + 30. The new success rate is given as 30%, which leads to an equation involving N. Solving this equation provides the initial number of matches, and adding 30 gives the total number of ODIs after the losing streak.

Step-by-Step Solution:
Step 1: Let the initial total number of ODIs between the teams be N. Step 2: Initial success rate for Pakistan is 60%, so wins initially = 0.60 * N. Step 3: Pakistan then loses the next 30 ODIs, so wins do not increase; they remain 0.60 * N. Step 4: Total matches after these 30 ODIs become N + 30. Step 5: After the losing streak, the success rate is 30%, so we have 0.60 * N / (N + 30) = 0.30. Step 6: Multiply both sides by (N + 30) to get 0.60 * N = 0.30 * (N + 30). Step 7: Expand the right-hand side: 0.60 * N = 0.30 * N + 9. Step 8: Subtract 0.30 * N from both sides: 0.30 * N = 9. Step 9: Solve for N: N = 9 / 0.30 = 30. Step 10: Total matches after the extra 30 ODIs = N + 30 = 30 + 30 = 60.

Verification / Alternative check:
With N = 30 initial matches, Pakistan initially wins 60% of 30, which is 18 matches. After that, Pakistan loses 30 matches in a row, so total matches become 60 and total wins remain 18. The final success rate is 18 / 60 * 100 = 30%. This matches the problem statement precisely, confirming that our calculation of N and the final total number of matches is correct and consistent with the given percentages.

Why Other Options Are Wrong:
If the total number of matches were 50, then after subtracting the last 30, the initial matches would be only 20, and winning 60% of 20 would give 12 wins. The final success rate would then be 12 / 50 * 100 = 24%, not 30%. For 45 total matches, a similar check fails. If the total number of matches were only 30, that would mean no earlier matches at all, which contradicts the initial 60% success rate. Therefore, 60 is the only value that makes all conditions hold true.

Common Pitfalls:
Some learners try to average success rates or subtract percentages directly rather than setting up and solving an equation. Others may forget that after 30 losses, the number of wins remains unchanged. Confusing the initial and final total matches can also lead to incorrect algebra. The safest method is to introduce variables, translate each verbal condition into a clear equation, and solve step by step as done here.

Final Answer:
The total number of ODIs played between the two countries after the 30 consecutive losses is 60.