Question

The average marks of the students in four sections A, B, C and D of a school is 60%. The average marks of the students of A, B, C and D individually are 45%, 50%, 72% and 80%, respectively. If the average marks of the students of sections A and B together is 48% and that of the students of B and C together is 60%, what is the ratio of the number of students in sections A and D?

• A. 2 : 3
• B. 4 : 3
• C. 5 : 3
• D. 3 : 5

Answer 1

Answer: (B)

4 : 3

Answer 2

Let $a,b,c,d$ be the number of students in A, B, C and D respectively

Given, average marks of the students in section A, B, C and D of the school = 60

Then $\frac{45a+50b+72c+80d}{a+b+c+d}=60\%$

$=45a+50b+72c+80d=60a+60b+60c+60d$

$=12c+20d=15a+10b..............(1)$

Average marks of the students of sections A and B together is $48\%$

$=\frac{45a+50b}{a+b}=48\%$

$=454a+50b=48a+48b$

$=3a=2b$ (or) $15a=10b.................(2)$

Average marks of the students of sections B and C together is $60\%$

$=\frac{72c+80d}{c+d}=60\%$

=\$72c+80d=60c+60d$

$=12c=12d..............(3)$

Substitute equations (2) and (3) in equation (1)

⇒ $20d+20d=15a+15a$

⇒ $40d=30a$

⇒ $a:d=4:3$

Hence, option B is the correct answer.The correct option is (B): 4 : 3