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
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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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