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In a cricket eleven, the average age ...

In a cricket eleven, the average age of eleven players 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, what is the age of the captain? (a) 33 years (b) 34 years (c) 35 years (d) 36 years

A

42 years

B

35 years

C

24 years

D

27 years

Text Solution

Verified by Experts

The correct Answer is:
B
We have
Mean of 11 players = `("Sum of age of eleven players "(S_(11)))/(11)`
`:. 28 = (S_(11))/(11) " "` (Given)
`rArr 28 xx 11 = S_(11) " "` . . . (i)
Mean of first group of 3 players `= ("Sum of ages of three players "(S_(3)))/(3)`
`rArr = (S_(3))/(3)` (Given )` rArr 25 xx 3 S_(3) " "` . . . (ii)
Also, Mean of second group of 3 players `= (S_(3))/(3)`
`rArr 28 xx 3 S._(3) " "` . . . (iii) (Given)
Mean of third group of 3 players ` = (S.._(3))/(3)`
`rArr 30 xx 3 = S.._(3) " "` . . . (iv) (Given)
Let the age of youngest player be x years
`:.` Age of captain = (x + 11) years
We have `S_(11) = S_(3) + S._(3) + S.._(3) +` Age of captain + Age of youngest player
`rArr 28 xx 11 = 25 xx 3 + 28 xx 3 + 30 xx 3 + (x + 11) + x " "` [Using (i), (ii), (iii), and (iv) ]
`rArr 308 - 75 - 84 - 90 = 2x + 11`
`rArr 59 - 11 = 2 x rArr x = 24` years
Thus, caption.s age `= (x + 11) = (24 + 11) = 35` years
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