Question

In a school, ratio of number of boys to that of girls was \(6:5.\) In the next year, number of boys increased by \(20\%\) and 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?

• A. \(680\)
• B. \(750\)
• C. \(770\)
• D. \(780\)

Answer 1

The Correct Option is C

Let the initial number of boys be \(6x\) and the number of girls be \(5x\), based on the given ratio \(6:5\). The total number of students initially is \(6x + 5x = 11x\).

The number of boys increased by \(20\%\), so the new number of boys is \(6x \times 1.2 = 7.2x\).

The number of girls increased by \(10\%\), so the new number of girls is \(5x \times 1.1 = 5.5x\).

The total number of students now is \(7.2x + 5.5x = 12.7x\).

The increase in the number of students is given as \(119\), thus:

\(12.7x - 11x = 119\)

\(1.7x = 119\)

Solving for \(x\), we get:

\(x = \frac{119}{1.7} = 70\)

Initially, the total number of students was:

\(11x = 11 \times 70 = 770\)

Therefore, the initial number of students in the school was 770.