Question

Q. Eleven batsmen score runs as follows:

i. The first five players together score 4 times the total score of the remaining players,

ii. The first six players together score 5 times the total score of the remaining players
and

iii. The average score of all eleven players is 30.

Find the score of sixth batsman

please let me know the answer of this Q​

Answer 1

1 )Given Number of players = 11,

Average score of 11 players = 30

Sum of the scores of 11 players = 11× 30

= 330 ---(1)

2 ) Let sum of the first 5 players score = x

sum of the remaining 6 players score = y

/* According to the problem given */

x = 4y ----(2)

Total score = 330 [ From (1) ]

=> x + y = 330 ---(3)

=> 4y + y = 330 [ From ( 2) ]

=> 5y = 330

=> y = 66 ---(4)

/* Put y = 66 in equation (3), we get */

x + 66 = 330

=> x = 330 - 66

=> x = 264 --(5)

3) Let Score of 6th batsman = k

x + k = 5(y-k)

=> x + k = 5y - 5k

=> 6k = 5y - x

=> 6k = 5×66 - 264 [From (4) and (5) ]

=> 6k = 330 - 264

=> 6k = 66

=> k = 11

Therefore.,

$\red { Score \:of \:the \:6th \:batsman} \green {= 11 }$

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Answer 2

6th Batsman had scored 11 runs