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
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