Question : The number of students in section A and section B of a class are 40 and 52, respectively. The average score in mathematics of all the students is 75. If the average score of the students in A is 20 % more than that of students in B then what is the average score of students in B?
Option 1: 71
Option 2: 65
Option 3: 69
Option 4: 63
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Correct Answer: 69
Solution :
Total number of students = 40 + 52 = 92
⇒ $75 = \frac{\text{(Sum of scores of all students)}}{92}$
⇒ Total score in mathematics = 75 × 92 = 6900
Now,
Let the average score of section B students be $x$
⇒ Average score of section A student = $x + \frac{20}{100} × x$
= $\frac{6x}{5}$
Now,
⇒ $x = \frac{\text{Sum of score of mathematics in section B}}{52}$
The sum of scores of section B in mathematics = $52x$
Now,
⇒ $\frac{6x}{5} = \frac{\text{Sum of score of mathematics in section A}}{40}$
Sum of score of mathematics in section A = $\frac{6x}{5} × 40=48x$
Now,
Total score = Sum of the scores of mathematics in section A + Sum of the scores of section B in mathematics
⇒ $6900 = 48x + 52x$
⇒ $100x = 6900$
⇒ $x = 69$
Hence, the correct answer is 69.
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