In a school, there were 1582 students and the ratio of the number of the boys and girls was 4: 3, After a few days. 30 girls joined the school but few boys left the school and as a result, the ratio of the boys and girls became 7: 6. The number of boys who left the school is:

Correct option is D

Given:
Number of students in school = 1582
Ratio of boys and girls = 4 : 3
Number of girls joined = 30
Let the ratio of boys and girls be 4x and 3x respectively.
Total number of boys and girls = 4x + 3x = 7x
Now, 7x = 1582

Number of boys

Number of girls

Now, some boys left and 30 girls joined the ratio becomes 7:6
Let the number of boys who left be y. Then,

6(904 - y) = 7(708)
5424 - 6y = 4956
5424 - 4956 = 6y
468 = 6y
y = 78
The number of boys who left the school is 78.