Solvd the First Set
1. Sum of top scores= 435
Sm of minimum scores=153
To find the maximum avg we have to maximize the other scores, for that the 6th top score should be highest so that rest can just preceed it.
Avg of top 6 scores 72.5 So to make 6ht highest score maximum the scores have to be 70 71 72 73 74 75
Now if we chose 16 nxt scores from 69 68 ... 54 Sum of these scores= 984
Two scores are 48 49 sum= 97
So total sum= 1669
Hence maximum avg = 55.6 (1)
2. Avg.=45.2
so total runs scored= 1356 minus the 6 highest scores(435) nd 48 49 scored by him we get runs the total of rest of scores to be 824
Now if we assume n fifties scored by him
Let the scores in fifties be 50 51 52 .. (n elements) (1)
Other scores b 0 1 2 3 ... (3062n elements) (2)
so summation of 1 & 2 we should get a score close to 824
By this we get n=14
Plus the 6 highest scores which all could be fifties
We get Total no. of Maximum Fifties=20 (4)
3. Let the two centuries be 100,101
So Total score scored in his next 4 highest scores = 435201= 234
Again to maximize the lowest score the 6th highest score should be maximum So the nxt top scores would be 57 58 59 60
6th highest is 57 rest can follow like nxt being 56 55 54 nd so on
The 30th score comes to be 33
So maximum highest lowest score would be 32 (3)
4. To maximize the highest score we have to minimize the rest of the top 5 scores
Now Sum of lowest 5 scores=153 We have to hav minimum 5th lowest score
so that rest of scores can follow it
So the minimm possible fifth lowest score is 33
nxt scores can follow as 34 35 36 nd so on till 2nd highest score = 57
So sum of 2nd highest score to 6th highest score= 57 + 56 ... + 53= 275
Highest score= 435275= 160 ( Didnt find any option)
5. Again we have to find the highest 6th score= 70 so that rest of the scores can follow
By this we get highest scores as 70 71 72 73 74 75
Now if we try to increse the highest score we have to decrease atleast 1 from all the scores(29 from total score) which would result in increase of only 5 in the highest score because sum of highest six scores also will have to be constant
So maximum highest score in this condition is 75 (1)
