(Euclid 2022, Question 3, CEMC - UWaterloo)

(a) A large water jug is $\frac{1}{4}$ full of water. After $24$ litres of water are added, the jug is $\frac{5}{8}$ full. What is the volume of the jug, in litres?
(b) Stephanie starts with a large number of soccer balls. She gives $\frac{2}{5}$ of them to Alphonso and $\frac{6}{11}$ of them to Christine. The number of balls that she is left with is a multiple of $9$. What is the smallest number of soccer balls with which Stephanie could have started?
(c) Each student in a math club is in either the Junior section or the Senior section. No student is in both sections.
Of the Junior students, $60\%$ are left-handed and $40\%$ are right-handed.
Of the Senior students, $10\%$ are left-handed and $90\%$ are right-handed.
No student in the math club is both left-handed and right-handed.
The total number of left-handed students is equal to the total number of righthanded students in the math club.
Determine the percentage of math club members that are in the Junior section.

Answer Submission Note(s)
Drop the percent sign in part (c) and separate your answers with a single space.