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XAT 2011 — QA & DI Question 22

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.

In a city, there is a circular park. There are four points of entry into the park, namely - P, Q, R and S. Three paths were constructed which connected the points PQ, RS, and PS. The length of the path PQ is 10 units, and the length of the path RS is 7 units. Later, the municipal corporation extended the paths PQ and RS past Q and R respectively, and they meet at a point T on the main road outside the park. The path from Q to T measures 8 units, and it was found that the angle PTS is 60 . Find the area (in square units) enclosed by the paths PT, TS, and PS.

Answer & solution

  • A

    36√3

  • B

    54√3

  • 72√3

  • D

    90√3

  • E

    None of the above

Solution

The following diagram represents the given scenario.

​​​​​​​

Let, TR = x

∴ 8 × 18 = x (7 + x)

∴ x2 + 7x – 144 = 0

∴ x = 9 or x = – 16

But x cannot be negative.

Hence, x = 9

A(∆TPS) = 12 × 18 × 16 × sin 60°

= 72√3 sq.units

Hence, option (c).

XAT 2011 QA & DI Q22: In a city, there is a circular park. There are four points of entry into the park, namely - P, Q, R and S. Thr — Solution | TheCATExam