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During a cricket match, India playing against NZ scored in the following manner:

Partnership | Runs scored

$1$st wicket$~~$ | $112$
$2$nd wicket | $58$
$3$rd wicket$~$ | $72$
$4$th wicket$~$ | $9$
$5$th wicket$~$ | $46$
$6$th wicket$~$ | $23$

So I suppose there were $7$ batsmen who got to bat... right?

(i) Find the average runs scored by the first four batsmen

(a) $83.5~~~$ (b) $60.5~~~$ (c) $66.8~~~$ (d) Cannot be determined

(ii) The maximum average runs scored by the first five batsmen could be

(a) $80.6~~~$ (b) $66.8~~~$ (c)$76~~~$ (d) Cannot be determined

(iii) The minimum average runs scored by the last five batsmen could be

(a) $53.6~~~$ (b) $44.4~~~$ (c) $66.8~~~$ (d) $0~~~$

(iv) If the fifth down batsman gets out for a duck, then find the average runs scored by the first six batsmen

(a) $67.1~~~$ (b) $63.3~~~$ (c) $48.5~~~$ (d) Cannot be determined

$$~$$ I'm stuck here...
I don't understand the solutions for the above questions. Could someone explain with step by step solutions for all the above questions please ?
Here you can find cricket rules, and here about Partnership...

Original Answers

(i) Original answer
Ans : (d)
Explanation : You don't know who got out when. Hence, cannot be determined

I don't know how to find out average runs scored by $1$st four batsmen because I don't know which batsman scored how much runs.

(ii) Original answer
Ans : (a)
Explanation : Since possibilities are asked about, you will have to consider all possibilities. Assume, the sixth and seventh batsmen have scored zero. Only then will the possibility of the first $5$ batsmen scoring the highest possible average rise. In this case the maximum possible average for the first $5$ batsmen could be $403/5 = 80.6$

$~~~~~$ Assume, the sixth and seventh batsmen have scored zero.

Does this mean there are only seven batsmen?

(iii) Original answer
Ans : (d)
Explanation : Again it is possible that only the first batsman has scored runs.

Okay ,but how did they get 0 ?

$[403$ (i.e scored by first batsman alone) $+ 0 + 0 + 0 + 0 + 0] /5 = 80.6$ ... Is this the way to calculate the minimum average runs scored by the last five batsmen assuming that only the first batsman has scored runs ? But according to the given answer this is wrong... I know this is wrong, but this is what i could think of :(

(iv)Original answer
Ans : (d)
Explanation : We cannot find out the number of runs scored by $7$th batsman. Hence the answer is d.

Thanks.

BusyAnt
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mac07
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    The batsman's score cannot be determined because there are two batsmen in cricket. Basically this question relies on knowledge of cricket. – Suzu Hirose Dec 26 '14 at 06:20
  • You are assuming that we all know the rules of cricket. While it might be true a large portion of the world's population (India+?), it is most likely not true for "this website's population". Please do form your question in a strictly mathematical manner, or specify the relevant rules of this games (former option being highly preferable). – barak manos Dec 26 '14 at 06:48
  • @barak manos should I post the rules here instead of giving a link? – mac07 Dec 26 '14 at 10:59
  • Forming your question in a strictly mathematical manner would be highly preferable. – barak manos Dec 26 '14 at 11:12
  • For (iii) the minimum possible calculation should be $\frac{0+0+0+0+0}{5}$ for the last five batsmen – Henry Sep 07 '17 at 22:00

1 Answers1

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I think that the answer should be $(d)$ because we don't know who went out when. There are a lot of orders possible which makes it difficult to find the runs scored by first four batsmen.

Possible orders may be:-

$x_1+x_2=112$, $x_2+x_3=58$, $x_3+x_4=72$, $x_4+x_5=92$, $x_5+x_6=46$, $x_6+x_7=23$

or,

$x_1+x_2=112$, $x_1+x_3=58$, $x_1+x_4=72$, $x_1+x_5=92$, $x_1+x_6=46$, $x_1+x_7=23$

and a lot more.

Dheeraj Kumar
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