Till a certain date, Pakistan has a success rate of 50% against India in all the ODIs played between two countries. Pakistan lost all the 30 ODIs played against India after that date, and so their success rate decreases to 40%. Find the total number of ODIs played between the two countries.12018060150
Question
Till a certain date, Pakistan has a success rate of 50% against India in all the ODIs played between two countries. Pakistan lost all the 30 ODIs played against India after that date, and so their success rate decreases to 40%. Find the total number of ODIs played between the two countries.12018060150
Solution
The problem can be solved using simple algebra. Let's denote:
- X as the total number of matches played between Pakistan and India till the certain date.
- Y as the total number of matches played between the two countries.
According to the problem, Pakistan had a success rate of 50% against India in all the ODIs played between the two countries till a certain date. This means that Pakistan won 50% of X matches, or 0.5X matches.
After that date, Pakistan lost all the 30 ODIs played against India. So, the total number of matches won by Pakistan remains the same (0.5X), but the total number of matches played increases by 30 (X + 30).
The problem also states that after losing these 30 matches, Pakistan's success rate decreases to 40%. This means that the number of matches won by Pakistan (0.5X) is 40% of the total number of matches played (Y). In other words, 0.5X = 0.4Y.
We can substitute Y = X + 30 into this equation to solve for X:
0.5X = 0.4(X + 30) 0.5X = 0.4X + 12 0.1X = 12 X = 120
Substitute X = 120 into Y = X + 30 to find Y:
Y = 120 + 30 Y = 150
So, the total number of ODIs played between the two countries is 150.
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