Question

The average marks of section A are 65 and that of section B is 70. If the average marks of both the sections combined are 67, then the ratio of the number of students of section A to that of section B is
(a) 1 : 2
(b) 3 : 2
(c) 5 : 9
(d) 16 : 1

Answer 1

Hint: To solve this type of problem we are to find the total sum of the given average. Find them and equalize both equations to get the ratio of the students of both sections. We will get the sum of the given averages in two ways.

Complete step by step solution:
Let the number of students in section A be ‘x’ and that in section B be ‘y’.
The average marks of section A is said to be 65 marks.
So, total marks of section A = 65x marks
The average marks of section B is said to be, 70 marks.
Total marks of section B = 70y marks
But the average marks of the sections combined is, 67 marks
And total number of students = (x + y)
So, total marks of both sections, 67 (x + y) marks.
Then,
\[\begin{array}{l}
65x + 70y = 67(x + y)\\
 \Rightarrow 65x + 70y = 67x + 67y\\
 \Rightarrow 2x = 3y\\
 \Rightarrow \dfrac{x}{y} = \dfrac{3}{2}
\end{array}\]
Our required ratio is, 3:2
Hence, the correct option is, (b) 3: 2

Note: If we get the ratio of x: y as a negative number then we have to understand that there is a mistake in the calculation. So, we have to check the calculations very carefully and then analyze the problem. The calculation mistakes can always be very lethal for easier problems.