Question

Eleven batsmen score runs as follows:
i. The rst ve players together score 4 times the total score of the remaining players;
ii. The rst 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 the sixth batsman.

Answer 1

Step-by-step explanation:

)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.,

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