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Read the given information and answer the question that follows.
In an institute, 1800 students are studying five different courses -A, B, C, D and E. The number of male students is $$57\frac{1}{7}\%$$ more than that of female students. Out of male total students, 24% are studying course B and the ratio of the number of female students to male students studying this course is 5:6. The total number of students studying course C is 342, out of which female students are 104.18% of female are studying course A and the ratio of male students to female students studying A is 4:3. One-fifth of total males are studying course D and the number of female students studying D is 25% less than that of males studying D.The remaining male and female students are studying course E.
The average number of female students studying courses A, B and C is approximately what per cent less than the total number of male students studying courses D and E?
It is giving that 1800 students are studying five different courses -A, B, C, D and E.
The number of male students is $$57\frac{1}{7}\%$$ more than that of female students.
Let number of female students be 100x, thus number of male students will be 100x+(400/7)x = 1100/7x
Total students = 1800
100x+1100x/7 = 1800
1800x/7 = 1800
x = 7
Thus, number of female students = 700 and number of male students = 1100
It is given that Out of male total students, 24% are studying course B = 24% of 1100 = 264
the ratio of the number of female students to male students studying this course is 5:6.
Number of female students studying course B = (264/6)*5 =220
Total students studying course B = 264+220 = 484
It is given that the total number of students studying course C is 342, out of which female students are 104. Hence, number of male students = 342 - 104 = 238
It is given that 18% of females are studying course A = 18% of 700 = 126
Also, the ratio of male students to female students studying A is 4:3.
Hence, the number of male students = (126/3)*4 = 168
Total students studying A = 168+126 = 294
It is also given that One-fifth of total males are studying course D = 20% of 1100 = 220
Also, the number of female students studying D is 25% less than that of males studying D = 220*0.75 = 165
Total number of students studying D = 165+ 220 = 385
Therefore, we make a table from the above information-
The average number of female students studying courses A, B and C = (126+220+104)/3 = 150
The total number of male students studying courses D and E = 220+210 = 450
The average number of female students studying courses A, B and C is approximately what per cent less than the total number of male students studying courses D and E = (300/450)*100 = 66.66% (Approx)Option A is the correct answer.
