Question

In an examination, the average marks of 4 girls and 6 boys is 24 . Each of the girls has the same marks while 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 2 girls and 6 boys is

• A. 20
• B. 22
• C. 21
• D. 19

Answer 1

The Correct Option is C

Considering that the mean score for four females and six guys is 24
Assume that 'b' denotes a boy's mark and 'g' represents a girl's mark. 
\(4g + 6b = 10\times24 = 240 ......(1)\)
We have, \(b≤g≤2b\).
The only possible values of \( 2g + 6b = 2g + 240 - 4g = 240 - 2g\) must be found. 
When b = g, 10g = 240, and g = 24, we can deduce (1).

the value of 240 - 2g varies from \(240 - 2\times24 - 240 - 2\times \frac{240}{7}\)
 when \(b = \frac{g}{2}\) 
\(⇒\) \(7g = 240\) 
\(⇒\) \(g =\frac{ 240}{7} \)
\(⇒\) 171.42 to 192 
\(⇒\) Integer values of 172 to 192 = 21 values