Try this beautiful problem from the PRMO, 2019 based on Lines and Angles.
On a clock, there are two instants between 12 noon and 1 pm when the hour hand and the minute hand are at right angles. the difference in minutes between these two instants written as a+\(\frac{b}{c}\) where a b c are positive integers with \(b\lt c\) and \(\frac{b}{c} \) in the reduced form. find a+b+c.
Lines
Algebra
Angles
Answer: is 51.
PRMO, 2019, Question 7
Higher Algebra by Hall and Knight
Minute hand turns 6 (in degrees) in 1 min and hour hand turns half (in degree) in 1 min
x min after 12 is 6x -\(\frac{x}{2}\)=90 or 270 (in degrees) then x =16\(\frac{4}{11}\) or 49\(\frac{1}{11}\)
Difference 32\(\frac{8}{11}\) then a+b+c=32+8+11=51.
Publishing original scientific research in a peer-reviewed journal is an achievement many scholars work toward for years. Achieving this feat early in one's academic journey requires exceptional intellectual rigor, creativity, and persistence. Aaditya Punatar and Muskan Sadana have reached this remarkable milestone, successfully publishing their collaborative research paper in the prestigious Journal of Emerging Investigators […]
Her project on quantum-accelerated Steiner trees for 15-minute cities earned a place among the finalists at the world's largest pre-college STEM competition. Prishaa Shrimali of Marymount School of New York, was selected as a Grand Finalist at the 2026 Regeneron International Science and Engineering Fair (ISEF) in Phoenix, Arizona. Her project was Optimizing Urban Accessibility: […]
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's M.Stat Entrance. They ranked within the first 50 in the entire country in these entrances. I.S.I. M.Stat Entrance
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's B.Stat Entrance and Chennai Mathematical Institute's B.Sc. Math Entrance. They ranked within the first 200 in the entire country in these entrances. Most of these students attended the problem solving workshops regularly, which happen 5 days every week. CMI B.Sc. Math Entrance […]