Multiple choice

Directions: The question given below is followed by two statements labelled I and II. You have to determine whether the data given in the statements is sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer. P and Q started running around a circular track of 1500 m in opposite directions from same point. How far would Q be from the starting point, when they both met the first time? (I) P took 10 min to run the circular track and Q took half the time taken by P. (II) The ratio of speed of P to that of Q was 1 : 2.

  1. The question can be answered using statement-I alone but cannot be answered using the other statement alone.

  2. The question can be answered using statement-II alone but cannot be answered using the other statement alone.

  3. The question can be answered using either of the statements alone.

  4. The question can be answered using both the statements together but cannot be answered using either of the statements alone.

  5. The question cannot be answered even using both the statements together.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To find how far Q is from the start, we need their speeds. Statement I gives P's time (10 min) and Q's time (5 min). We can find speeds. Statement II gives the ratio of speeds directly. Both are sufficient to find the relative speed and the time to meet.

AI explanation

Let the total distance of the track be 1500 m. From statement I, P takes 10 min so P's speed is 150 m/min and Q takes half the time, making Q's speed 300 m/min, which means when they meet they have covered distances in a 1 to 2 ratio, and since they run in opposite directions, Q covers 1000 m from the starting point. Statement II gives the ratio of their speeds directly as 1 to 2, which means they cover distances in a 1 to 2 ratio, yielding the exact same result of 1000 m for Q. Thus, the question can be answered using either of the statements alone.

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