Try this beautiful problem on balls based on Number theory, useful for ISI B.Stat Entrance.
A bag contains colored balls of which at least 90% are red. Balls are drawn from the bag one by one and their color noted. It is found that 49 of the first 50 balls drawn are red. Thereafter 7 out of every 8 balls are red. The number of balls in the bag can not be
Number theory
Percentage
Inequility
Answer: (b) \(210\)
TOMATO, Problem 128
Challenges and Thrills in Pre College Mathematics
Let the number of balls in the bag is n.Let, m number of times 8 balls are drawn. Therefore, \(n = 50 + 8m\). Red balls =\( 49 + 7m\)
Can you now finish the problem ..........
Percentage of red balls = \(\frac{(49 + 7m)}{(50 + 8m)}≥ \frac{90}{100}\)
\(\Rightarrow \frac{(49 + 7m)}{(50 + 8m)}≥0.9\)
\(\Rightarrow 49 + 7m ≥ 45 + 7.2m\)
\(\Rightarrow 0.2m ≤ 4\)
\(\Rightarrow m ≤ 20\)
\(\Rightarrow n ≤ 50 + 8 \times 20 = 210\)
Therefore we can say that at most \(210\) balls can be drawn. So there must be at most \(210\) balls in the bag, and so there cannot be \(250\) balls in the bag (because \(250>210\)).
Therefore option (C) is the correct answer
AMC - AIME Boot Camp... for brilliant students.
Use our exclusive one-on-one plus group class system to prepare for Math Olympiad
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 […]
In 2025, 8 students from Cheenta Academy cracked the prestigious Regional Math Olympiad. In this post, we will share some of their success stories and learning strategies. The Regional Mathematics Olympiad (RMO) and the Indian National Mathematics Olympiad (INMO) are two most important mathematics contests in India.These two contests are for the students who are […]
Cheenta Academy proudly celebrates the success of 27 current and former students who qualified for the Indian Olympiad Qualifier in Mathematics (IOQM) 2025, advancing to the next stage — RMO. This accomplishment highlights their perseverance and Cheenta’s ongoing mission to nurture mathematical excellence and research-oriented learning.