Question : The average mark scored by 8 boys is 72. If the scores of three girls are also included, the average marks increase by 3. The average marks scored by the three girls are:
Option 1: 95
Option 2: 83
Option 3: 78
Option 4: 68
Correct Answer: 83
Solution :
The average mark scored by 8 boys is = 72
If the scores of three girls are also included,
The average marks increase by = 3
Average = $\frac{\text{Sum of all the observations}}{\text{Total no. of observations}}$
Let the average marks of the three girls be $x$.
Then, the total average is,
75 = $\frac{(72\times 8)+3\text{$x$}}{11}$
Solving for $x$,
$x$ = $\frac{(75\times 11)-(72\times8)}{3}$ = 83
$\therefore$ The average mark of the three girls is 83.
Hence, the correct answer is 83.
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