Question

What is the least number of innings in which 20 or 30 runs were scored (all players taken together)?

• A. 3
• B. 4
• C. 5
• D. None of these

Answer 1

The correct option is C

5

In case of Pujara:
Lowest score = 30
Highest score = 90
Average score = 50
$\therefore$ Total score if he played 2 innings = 50 $\times$ 2 = 100
(But 90 + 30 = 120; therefore there are more than 2 innings played)
$\therefore$ Third innings score 150 - (90 + 30)= 30 runs
Hence, Pujara played minimum 3 innings with scores of 30, 30 and 90 runs repectively.
Similarly, minimum innings for other players can also be calculated:
$\begin{array}{cc}\text{Vijay}& \text{Lowest}=20,\text{highest}=80,\text{average}=50\\ & \text{Minimum innings}=2(20\text{runs},80\text{runs})\\ \text{Pujara}& \text{Lowest}=30,\text{highest}=90,\text{average}=50\\ & \text{Minimum innings}=3(30\text{runs},30\text{runs},90\text{runs})\\ \text{Kohli}& \text{Lowest}=10,\text{highest}=60,\text{average}=30\\ & \text{Minimum innings}=3(10\text{runs},20\text{runs},60\text{runs})\\ \text{Rahane}& \text{Lowest}=20,\text{highest}=70,\text{average}=40\\ & \text{Minimum innings}=3(20\text{runs},30\text{runs},70\text{runs})\\ \text{Sharma}& \text{Lowest}=10,\text{highest}=30,\text{average}=20\\ & \text{Minimum innigs}=2(10\text{runs},30\text{runs})\end{array}$
To minimise the number of 20's and 30's we can have following table.
$\begin{array}{cc}Vijay& 20,80\\ Pujara& 30,40,40,90\\ Kohli& 10,10,40,60\\ Rahane& 20,30,70\\ Sharma& 10,30\end{array}$
Minimum innings of 20's or 30's = 1+1+0+2+1=5