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CAT 1996 — QA Question 21

Basics of QuadrilateralsEasy
Passage / Data

Direction: Answer the questions based on the following information.

A salesman enters the quantity sold and the price into the computer. Both the numbers are two-digit numbers. But, by mistake, both the numbers were entered with their digits interchanged. The total sales value remained the same, i.e. Rs. 1,148, but the inventory reduced by 54.

The figure shows the rectangle ABCD with a semicircle and a circle inscribed inside in it as shown. What is the ratio of the area of the circle to that of the semicircle?

Answer & solution

  • A

    (2-1)2:1

  • B

    2(2-1)2:1

  • C

    (2-1)2:2

  • None of these

Solution

Let radius of the semicircle be R and radius of the circle be r.
Let P be the centre of semicircle and Q be the centre of the circle.
Draw QS parallel to BC.
Now, ΔPQS ~ ΔPBC

∴PQPB=QSBC⇒R+r2R=R-rR⇒R+r=2R-2r⇒r(1+2)=R(2-1)

⇒r=R(2-1)(2+1)×(2-1)(2-1)

⇒r=R(2-1)2

Required Ratio = πr2πR2×2

=πR2(2-1)4×2πR2

=2(2-1)4:1

CAT 1996 QA Q21: The figure shows the rectangle ABCD with a semicircle and a circle inscribed inside in it as shown. What is th — Solution | TheCATExam