In a school, the ratio of the number of boys to that of girls was 6 : 5. In the next year, the number of boys increased by 20% and the number of girls increased by 10% resulting in an increase of 119 students in the school. How many students were there in the school initially?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 770
A ratio of 6 : 5 means the boys and girls are 6 and 5 times a common number; the increase of 119 students fixes that number.
Assuming the number of boys to be \(6k\) and of girls \(5k\):
Increase in boys: 20% of \(6k=1.2k\)
Increase in girls: 10% of \(5k=0.5k\)
\(1.2k+0.5k=1.7k=119\), so \(k=70\)
Students at first \(=6k+5k=11k=11\times70=770\)