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20 Feb 2024, 01:04
Kudos
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D
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Difficulty:
95%
(hard)
Question Stats:
36% (03:42) correct
64%
(02:41)
wrong
based on 28
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In an examination, the average marks of 8 girls and 10 boys is 25. Each of the girls has the same marks and each of the boys has the same marks. If the marks of any girl is at most double the marks of any boy, but not less than the marks of any boy, then the number of possible distinct integer values of the total marks of 4 girls and 8 boys is :
A. 18
B. 20
C. 21
D. 24
E. 25
A. 18
B. 20
C. 21
D. 24
E. 25
20 Feb 2024, 03:32
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Shubhradeep
8g + 10b = 25*18
Incase the marks are the maximum, that is each girl is double that of each boy. => g=2b
8*2b + 10b = 25*18 = 450.........26b = 450........b = 450/26 = 17.30
Marks of 4 girls and 8 boys 4*2b+8b = 16b = 16*17.30 = 276.92
Incase the marks are the minimum, that is eacg girl is equal to that of each boy. => g=b
8*b + 10b = 25*18 = 450........18b = 450.......b=450/18 = 25
Marks of 4 girls and 8 boys => 4*b+8b = 12b = 12*25 = 300
So, the possible numbers are 276.92 to 300, which contains 24 integer values.
D
20 Feb 2024, 03:55
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chetan2u
For the second case
\(g\geq{b}\) so minimum value of g i.e, g=b
that gets us
b = 25
