Question

The problem below consists of a question and two statements numbered 1 & 2. You have to decide whether the data provided in the statements are sufficient to answer the question.
In a cricket match, three slip fielders are positioned in a straight line. The distance between the 1st slip and the 2nd slip is the same as the distance between the 2nd slip and the 3rd slip. The player X, who is not on the same line of slip fielders, throws a ball to the 3rd slip and the ball takes 5 seconds to reach the player at the 3rd slip. If he had thrown the ball at the same speed to the 1st slip or to the 2nd slip, it would have taken 3 seconds or 4 seconds, respectively. What is the distance between the 2nd slip and player X?
1. The ball travels at a speed of 3.6 km/hour.
2. The distance between the 1st slip and the 3rd slip is 2 meters.

• A. Statement 1 alone is sufficient to answer the question, but statement 2 alone is not sufficient
• B. Statement 2 alone is sufficient to answer the question, but statement 1 alone is not sufficient.
• C. Each statement alone is sufficient.
• D. Both statements together are sufficient, but neither of them alone is sufficient.
• E. Statements 1 & 2 together are not sufficient.

Answer 1

Answer: (E)

To determine whether the data provided in the statements are sufficient to answer the question, let's analyze each statement independently and then together.

• Given: The player X throws the ball at a constant speed to three slip fielders.

1. Evaluating Statement 1:
   • The ball travels at a speed of 3.6 km/hour. We need to convert this speed into meters per second for consistency with the given time values. \[ \text{Speed in m/s} = \frac{3.6 \times 1000}{3600} = 1 \text{ m/s} \]
   • Using the formula \( \text{Distance} = \text{Speed} \times \text{Time} \),
     • To 1st slip: Distance = \(1 \times 3 = 3\) meters
     • To 2nd slip: Distance = \(1 \times 4 = 4\) meters
     • To 3rd slip: Distance = \(1 \times 5 = 5\) meters
   • However, we don’t know the exact distance between the slip fielders as this statement only gives the speed and times to each slip.
2. Evaluating Statement 2:
   • The distance between the 1st slip and the 3rd slip is 2 meters.
   • This implies that the distance between each consecutive pair of slip fielders (1 to 2 and 2 to 3) is \(1\) meter since they are in a straight line and the distance is equally split.
   • However, we lack information about the speed at which the ball is thrown to determine the distance from player X to the 2nd slip.

• Combining Statements 1 & 2:
  • Using both statements, we know the speed (1 m/s) and can calculate each distance the ball travels, but knowing each leg's distance from statement 2 (1 meter between each pair of slips) does not help without comparisons specifically needed from X to 2nd slip.
  • The combined data lacks enough to connect the position of player X directly to the known fixed distances across the slip fielders.

Therefore, the given data in both statements together are insufficient to answer the question about the distance from player X to the 2nd slip. The correct answer is both statements together are not sufficient.

Answer 2

The ball takes 5 seconds, 4 seconds, and 3 seconds, respectively, to reach the 3^rd slip, 2^nd slip, and 1^st slip.
Let the distance between X and 3^rd slip, 2^nd slip, and 1^st slip, respectively, be 5a meters, 4a meters, and 3a meters, and let the distance between 1^st and 2^nd, 2^nd and 3^rd slip be ‘d’ meters.
According to the question:

Using the Apollonius theorem,
(5a)² + (3a)² = 2(4a)² + 2(d)²
2a² = 2d²
or, a = d
But (3a, 2a, 5a) cannot form a triangle and X is not on the same line contradicting each other. Hence, the question is incorrect.