Question:medium

A ship was moving towards lighthouse on the shore with uniform speed. A man standing on the lighthouse observes the ship. Eight minutes later, he finds that the angle of depression was 45°. In how much time does the ship reach the lighthouse?
Statement 1: Initially, the man standing on the lighthouse observes the ship at an angle of depression of 30°
Statement 2: The speed of the ship was 6 km/h and the height of the lighthouse is 300 m
Directions: This question has a problem and two statements numbered (1) and (2) giving certain information. You have to decide if the information given in the statements is sufficient for answering the problem. Indicate your answer

Updated On: Jun 30, 2026
  • statement (1) alone is sufficient to answer the question
  • statement (2) alone is sufficient to answer the question
  • both the statements together are needed to answer the question
  • either statement (1) alone or statement (2) alone is sufficient to answer the question
  • neither statement (1) nor statement (2) suffices to answer the question
Show Solution

The Correct Option is D

Solution and Explanation

The correct answer is option (D):
either statement (1) alone or statement (2) alone is sufficient to answer the question

Let's analyze the problem. We have a ship approaching a lighthouse, and we want to find the time it takes to reach the lighthouse from a certain point. We know the angle of depression changes from some initial angle to 45 degrees in 8 minutes.

We can model this using right triangles. The height of the lighthouse is a constant. The distance of the ship from the lighthouse is changing. We are concerned with the ratio of these distances.

We can denote the initial distance of the ship as 'd1', the distance after 8 minutes as 'd2'. We are given that at time t1 the angle of depression is angle1 and at time t1+8 minutes the angle is 45 degrees.

The horizontal distance from the lighthouse and the height are involved. Since the ship is moving with uniform speed, we can say that the distance covered by the ship in a given time interval will be proportional to time.

Statement 1: Provides the initial angle of depression (30 degrees). Using this and the fact that the angle of depression becomes 45 degrees after 8 minutes, we have all the information required to solve for the final time. We know that the ship travels a certain distance in 8 minutes, and we know the relationships between the distances and angles. This is sufficient to solve for the total time required for the ship to reach the lighthouse. We can set up two right triangles and create equations involving distances and angles. The ratio between the distances is sufficient to calculate the time

Statement 2: Provides the speed of the ship (6 km/h) and the height of the lighthouse (300 m).
Using the height of the lighthouse and the angle of depression information, we can calculate the distance traveled in 8 minutes. With the speed, we can calculate the remaining time required. This is also sufficient to solve for the time.

In both cases, we can form equations and solve. Therefore, either statement (1) alone or statement (2) alone is sufficient to answer the question.
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Top Questions on Statements and Inferences

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