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Football goals average calculation

CAT 2021 Slot 2 · Quantitative Ability · Easy · Linear Equations

This is an easy Quantitative Ability question from the CAT 2021 Slot 2 paper. It tests Linear Equations. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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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

10

Explanation

Let nn be the number of matches already played and GG be the goals scored so far. Total matches after 10 more matches = n+10n + 10.

Scenario 1: 1 goal scored in next 10 matches. G+1n+10=0.15\frac{G + 1}{n + 10} = 0.15 G+1=0.15(n+10)G + 1 = 0.15(n + 10)

Scenario 2: 2 goals scored in next 10 matches. G+2n+10=0.2\frac{G + 2}{n + 10} = 0.2 G+2=0.2(n+10)G + 2 = 0.2(n + 10)

Subtract Scenario 1 from Scenario 2: 1=0.05(n+10)1 = 0.05(n + 10) n+10=10.05=20n + 10 = \frac{1}{0.05} = 20 n=10n = 10.

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