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CAT 1991 — QA Question 50

Time, Speed & DistanceEasy
Passage / Data

Answer the following questions based on the information given below:

There were a hundred schools in a town. Of these, the number of schools having a play – ground was 30, and these schools had neither a library nor a laboratory. The number of schools having a laboratory alone was twice the number of those having a library only. The number of schools having a laboratory as  well as a library was one fourth the number of those having a laboratory alone. The number of schools  having either a laboratory or a library or both was 35.

Each of these items has a question followed by two statements. As the answer,

Type 1, If the question can be answered with the help of statement I alone,
Type 2, If the question can be answered with the help of statement II alone,
Type 3, If both the statement I and statement II are needed to answer the question, and
Type 4, If the question cannot be answered even with the help of both the statements.

A train started from Station A, developed engine trouble and reached Station B, 40 minutes late. What is the distance between Stations A and B?

  1. The engine trouble developed after travelling 40 km from Station A and the speed reduced to 1/4th of the original speed.
  2. The engine trouble developed after travelling 40 km from station A in two hours and the speed reduced to ¼th of the original speed.

Answer & solution

  • A

    1

  • 2

  • C

    3

  • D

    4

Solution

In order to solve the question, we need to know two things :

(a) the original speed of the train or the new speed of the train and

(b) at what distance from A or after how much time after leaving A the train brokedown.

The statement II provides both of these data viz. original speed = 20 kmph and distance from A = 40 kms. and hence only this is required to answer the question.

For e.g: If the distance between A & B is considered to be x, then time taken had it not broken down is x/20 hours.

The new time taken is [2 + (x – 40)/5] hours and we know that this time is 40 min. more than the original time.

The equation becomes : x/20 + 40/60 = [2 + (x – 40)/5], which can be easily solved to get value of x.

Hence, 2.

CAT 1991 QA Q50: Each of these items has a question followed by two statements. As the answer, Type 1, If the question can be a — Solution | TheCATExam