Question : The average mark scored by three students in a test was 55. When two more students ( A and B ) were added, the new average marks were reduced by 5. If B scores 15 marks more than A, what were the marks scored by A?
Option 1: 33
Option 2: 35
Option 3: 40
Option 4: 30
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Correct Answer: 35
Solution :
Average marks of 3 students = 55
Use the formula to find the average, Average = $\frac{\text{Sum of the marks}}{{\text{Total number of students}}}$
The sum of the Marks = Average × Total number of students
Sum of marks of 3 students = 55 × 3 = 165
When (A and B) are added, the average marks become = 55 – 5 = 50
Sum of marks of 5 students = 50 × 5 = 250
Marks of A and B = 250 – 165 = 85
Let marks of A = $x$,
If B scores 15 marks more than A, B = $x+15$
$\therefore x+x+15=85$
⇒ $2x+15=85$
$\therefore x=35$
Hence, the correct answer is 35.
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