Question 2

In a cricket team of 11 players, the average age is 28 years. Out of these, the average ages of three groups of three players each are 25 years, 28 years, and 30 years respectively. If in these groups, the captain and the youngest player are not included and the captain is eleven years older than the youngest player, then the age of the captain is

Solution

Team has 11 players with average of 28 years age :
$$X_1+X_2+......X_{11}$$ = 28(11)

Group I : $$X_1+X_2+X_3$$ = 25(3)
Group II : $$X_4+X_5+X_6$$ = 28(3)
Group III : $$X_7+X_8+X_9$$ = 3(30)

Let the non included Youngest players age be $$X_{10}$$ & Captain age be $$X_{11}$$.
Hence, it is given that , $$X_{11}=11+X_{10}$$.

Hence, 75 + 90 + 84 + $$X_{10}$$ + 11 + $$X_{10}$$ = 28(11)
it implies, $$X_{10}=24$$

Therefore, the Captain age ($$X_{11}$$) = 11+$$X_{10}$$. = 11 + 24 = 35

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