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In a college entrance test, the average marks obtained by all 30 boys of the class is 5 less than the average marks obtained by all 20 girls of the class. If the average marks of the whole class are 25, then find the ratio of average marks of boys to that of girls.
41 : 32
23 : 28
32 : 41
28 : 23
23 : 28
Use the alligation ratio: the ratio of number of boys to girls (3:2) must be inversely proportional to the deviations from the class average (25). Let girls' average be x+5, boys' x. Then 30x+20(x+5)=50├Ч25. Solving 50x+100=1250 gives 50x=1150, x=23. Boys = 23, Girls = 28.
Number of boys = 30, Number of girls = 20, Average marks of whole class = 25, Average of boys is 5 less than average of girls.
AtotalтАЛ=n1тАЛ+n2тАЛn1тАЛA1тАЛ+n2тАЛA2тАЛтАЛ
Use the alligation ratio: the ratio of number of boys to girls (3:2) must be inversely proportional to the deviations from the class average (25). Let girls' average be x+5, boys' x. Then 30x+20(x+5)=50├Ч25. Solving 50x+100=1250 gives 50x=1150, x=23. Boys = 23, Girls = 28.
Confusing the '5 less' relation and accidentally assigning the lower average to the girls instead of the boys.
Define variables
Let the average marks of girls be G and the average marks of boys be B. Given B=GтИТ5.
B=GтИТ5
Apply average formula
The total marks of the class is the sum of total marks of boys and girls. Total students = 30+20=50. Given class average = 25.
50├Ч25=30B+20G
Solve for G
Substitute B=GтИТ5 into the equation: 1250=30(GтИТ5)+20G. Simplifying, 1250=30GтИТ150+20G, so 1400=50G. Thus, G=28.
G=28
Find B and Ratio
Calculate boys' average: B=28тИТ5=23. The ratio of boys' average to girls' average is 23:28.
Ratio=2823тАЛ
B is correct because the average marks of boys is 23 and the average marks of girls is 28, resulting in a ratio of 23:28.
This type of weighted average problem is common in Mixture and Alligation topics. Always verify if the calculated average lies between the individual averages of the two groups.
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