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Save Rate

Problem

During a football match in a tournament a goalkeepers save rate was given as 33%. After saving the next shot on target it rose to 40%. How many more shots on target does he need to save to raise his save rate to 50%?


Solution

A save rate of 33% means 1 in 3, 2 in 6, 3 in 9, etc. (assuming 33% has been rounded down from 33.333...%).
i.e. 1/3 = 2/6 = 3/9 = 4/12 = ...

If the next shot on target was a save, both the numerator and denominator will have increased by 1.
40% = 2/5 = 4/10 = 6/15 = ...

We can see that 3 + 1/9 + 1 = 4/10, so the goalkeeper must currently have a save rate of 4 out of 10 shots on target.

If all subsequent shots on target are saved,
4/10 maps 5/11 maps 6/12 = 1/2 = 50%.

So it will necessary to save the next two shots on target.

What happens if one of the next two shots on target are not saved?

Problem ID: 102 (Feb 2003)     Difficulty: 2 Star

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