Let the number of blue balls be x.
Number of red balls = 5
Total number of balls = x + 5
P (getting a red all) = 5/(5 + x)
P (getting a blue ball) = x/(5 + x)
Given that,
2(5/(5 + x)) = (x/(5 + x)) ⇒ 10(x + 5) = x² + 5x – 50 = 0
⇒ x² – 10x + 5x – 50 = 0 ⇒ x(x – 10) + 5(x – 10) = 0
⇒ (x – 10)(x + 5) = 0
⇒ Either x – 10 = 0 or x + 5 = 0
⇒ x – 10 or x = -5
However, the number of balls cannot be negative.
Hence, number of blue balls = 10