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.
Best Answer
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.