CAT 2021 Slot 2 · Quant · Question 14
CAT 2021 Slot 2 previous year question on Averages, Mixture and Alligation, with the answer and a step-by-step solution.
In a football tournament, a player has played a certain number of matches and 10 more matches are to be played. If he scores a total of one goal over the next 10 matches, his overall average will be 0.15 goals per match. On the other hand, if he scores a total of two goals over the next 10 matches, his overall average will be 0.2 goals per match. The number of matches he has played is
Answer & solution
Answer: 10
Let him have played m matches so far, scoring g goals. In both scenarios the final number of matches is the same, m+10.
\frac{g+1}{m+10}=0.15 and \frac{g+2}{m+10}=0.2.
Subtracting kills g at once: \frac{1}{m+10}=0.05, so m+10=20 and m=10.
(As a check, g+1=0.15\times 20=3, so g=2 goals in his first 10 matches.)
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