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XAT 2011 — QA & DI Question 20

Simple EquationsEasy
Passage / Data

Answer the following question based on the information given below.

A man standing on a boat south of a light house observes his shadow to be 24 meters long, as measured at the sea level. On sailing 300 meters eastwards, he finds his shadow as 30 meters long, measured in a similar manner. The height of the man is 6 meters above sea level.

There are four machines in a factory. At exactly 8 pm, when the mechanic is about to leave the factory, he is informed that two of the four machines are not working properly. The mechanic is in a hurry, and decides that he will identify the two faulty machines before going home, and repair them next morning. It takes him twenty minutes to walk to the bus stop. The last bus leaves at 8:32 pm. If it takes six minutes to identify whether a machine is defective or not, and if he decides to check the machines at random, what is the probability that the mechanic will be able to catch the last bus?

Answer & solution

  • A

    0

  • B

    16

  • C

    14

  • 13

  • E

    1

Solution

If the mechanic wants to catch the bus, he will have 12 minutes to inspect the machines. As inspecting one machine takes 6 minutes, he will be able to identify the faulty machines if the first two machines he inspects are both faulty or both working properly.

Suppose A, B, C and D are the machines, and A and B are faulty. He can inspect these machines in 4P4 = 24 ways. If he inspects A and B first, he will be able to catch the bus. If he inspects C and D first, he will know that A and B are faulty and still he will be able to catch the bus.

There are 4 ways in which he can inspect A and B first and 4 ways in which he can inspect C and D first.

∴ Probability that he will be able to catch the bus

= 824 = 13

Hence, option (d).

XAT 2011 QA & DI Q20: There are four machines in a factory. At exactly 8 pm, when the mechanic is about to leave the factory, he is — Solution | TheCATExam