Directions: Each of the questions below consists of a statement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements is/are sufficient to answer the question. Read both the statements and Give answer (a) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question; Give answer (b) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question; Give answer (c) if the data either in Statement I or in Statement II alone are sufficient to answer the question; Give answer (d) if the data even in both Statements I and II together are not sufficient to answer the question; and Give answer (e) if the data in both Statements I and II together are necessary to answer the question. Two towns are connected by railway. Can you find the distance between them? I. The speed of mail train is 12 km/hr more than that of an express train. II. A mail train takes 40 minutes less than an express train to cover the distance.

if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question

if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question

if the data either in Statement I or in Statement II alone are sufficient to answer the question

if the data in both Statements I and II together are necessary to answer the question

[Solved] Directions: Each of the questions below consists of

Answer

Correct Answer: if the data even in both Statements I and II together are not sufficient to answer the question

Explanation

### Concept & Logic When comparing two moving bodies covering the same distance, the relationship between their speeds, times, and distance can be modeled with the time difference formula: $$ \Delta t = \frac{d}{v_1} - \frac{d}{v_2} $$ To solve for distance ($d$), we need exact values for both speeds, or at least one speed and the exact time. ### Step-by-Step Solution Let the distance be $d$ km. Let the speed of the express train be $v$ km/hr, and the time it takes be $t$ hours. From Statement I: * Speed of mail train = $(v + 12)$ km/hr. * No information is provided about time or distance. Not sufficient alone. From Statement II: * Time taken by mail train = $(t - \frac{40}{60})$ hours. * No information is provided about speeds. Not sufficient alone. Combining Statements I and II: * We can set up the equation: $\frac{d}{v} - \frac{d}{v + 12} = \frac{40}{60}$ * This gives us one equation with two unknown variables ($d$ and $v$). * Since we cannot determine unique values for two variables from a single equation, the distance cannot be calculated. ### Exam Strategy & Shortcut Count the variables. We have distance, speed, and time difference. We are given the speed difference and the time difference, leaving two unknown variables (base speed and distance) and only one relation. A unique solution is mathematically impossible. You can confidently select "not sufficient". ### Common Pitfall A common mistake is assuming that having differences in both speed and time is enough to solve for distance. This only works if you already know one of the absolute values (either a specific speed or a specific time). ### Final Answer Therefore, the correct answer is **if the data even in both Statements I and II together are not sufficient to answer the question**.