In a class of 45 students, the ratio of boys to girls is \(5:4\).
Consider the following statements:
I. If 5 more girls join the class, the ratio of boys to girls becomes \(1:1\).
II. If 9 more boys join the class, the ratio of boys to girls becomes \(17:10\).
Which of the above statements is/are correct?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Both I and II
First find the actual numbers from the ratio: boys \(=\displaystyle\frac{5}{9}\times45=25\), girls \(=\displaystyle\frac{4}{9}\times45=20\). Then apply the change and simplify.
I. If 5 more girls join the class, the ratio of boys to girls becomes \(1:1\). — Correct. There are then 25 boys and 25 girls.
Girls \(=20+5=25\)
Ratio \(=25:25=1:1\)
II. If 9 more boys join the class, the ratio of boys to girls becomes \(17:10\). — Correct. 34 boys to 20 girls simplifies to \(17:10\).
Boys \(=25+9=34\)
Ratio \(=34:20=17:10\)