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XAT 2011 — QA & DI Question 18

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.

A 25 ft long ladder is placed against the wall with its base 7 ft from the wall. The base of the ladder is drawn out so that the top comes down by half the distance that the base is drawn out. This distance is in the range:

Answer & solution

Correct answer: None of the above

  • A

    (2, 7)

  • B

    (5, 8)

  • C

    (9, 10)

  • D

    (3, 7)

  • None of the above

Solution

​​​​​​​

​​​​​​​

Let the base is drawn by x unit.

∴ Height of top of the ladder will decrease by x2.

∴ By Pythagoras theorem,

∴(24-x2)2 + (7+x)2 = 625

∴x24 + x2 - 24x + 14x = 0

∴5x24 = 10x

∴ x = 8

Hence, option (e).

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XAT 2011 QA & DI Q18: A 25 ft long ladder is placed against the wall with its base 7 ft from the wall. The base of the ladder is dra — Solution | TheCATExam