To find the number of boys in the group, we need to first calculate the total marks obtained by both the groups combined. We can do this by using the formula:

Total Marks = Average * Number of Students

For the group of 30 girls, the average marks are given as 80. Therefore, the total marks obtained by the girls can be calculated as:

Total Marks obtained by girls = 80 * 30 = 2400

Similarly, for the group of boys, the average marks are given as 70. Therefore, the total marks obtained by the boys can be calculated as:

Total Marks obtained by boys = 70 * Number of Boys


Now, we need to find the number of boys in the group. We can use the information given in the question that the combined average marks of both the groups is 76. We can use this to form an equation:

Total Marks obtained by girls + Total Marks obtained by boys = Combined Total Marks

Substituting the values we obtained earlier, we get:

2400 + 70 * Number of Boys = Combined Total Marks

We know that the combined average marks are 76, which means that the combined total marks can be calculated as:

Combined Total Marks = 76 * (30 + Number of Boys)

Substituting this value in the equation above, we get:

2400 + 70 * Number of Boys = 76 * (30 + Number of Boys)

Simplifying this equation, we get:

2400 + 70 * Number of Boys = 2280 + 76 * Number of Boys

Solving for Number of Boys, we get:

Number of Boys = (2400 - 2280) / (76 - 70) = 20

Therefore, there are 20 boys in the group.