Question

Two boys A and B find the jumble of ropes lying on the floor. Each takes hold of one loose end randomly. If the probability that they are both holding the same rope is one upon 101, then the number of ropes is equal to:

(a) 50
(b) 100
(c) 101
(d) 102

Answer 1

The number of ropes is equal to 101.

Step-by-step explanation:

To find the number of ropes given the probability that both boys are holding the same rope, we can set up an equation based on the probability.

1. Let the number of ropes be represented by x.
2. The probability that both boys are holding the same rope is 1/101, which can be written as 1/x * 1/(x-1).
3. Simplifying the equation, we get 1/x * 1/(x-1) = 1/101.
4. Cross-multiplying, we have (x-1) * x = 101.
5. Expanding, the equation becomes x^2 - x - 101 = 0.
6. Solving for x using the quadratic formula, we find that x is approximately 101. Therefore, the number of ropes is equal to 101.