CAT 1991 — QA Question 23
Use the following information:
Prakash has to decide whether or not to test a batch of 1000 widgets before sending them to the buyer. In case he decides to test, he has two options: (a) Use test I ; (b) Use test II. Test I cost Rs. 2 per widget. However, the test is not perfect. It sends 20% of the bad ones to the buyer as good. Test II costs Rs. 3 per widget. It brings out all the bad ones. A defective widget identified before sending can be corrected at a cost of Rs. 25 per widget. All defective widgets are identified at the buyer’s end and penalty of Rs. 50 per defective widget has to be paid by Prakash.
A circle is inscribed in a given square and another circle is circumscribed about the square. What is the ratio of the area of the inscribed circle to that of the circumscribed circle?
Answer & solution
- A
2 : 3
- B
3 : 4
- C
1 : 4
1 : 2
As it is apparent from the following diagram, the diameter of the inscribed circle is equal to the side of the square, while the diameter of the circumscribed square is equal to the diagonal of the square.
Since the ratio of any two circles is equal to the ratio of the squares of their diameters, in this case the required ratio is equal to (side)2 : (diagonal)2
If the side of the square is a, its diagonal will be √2a
Now, the ratio of the side to the diagonal of a square = 1 : √2, the ratio of their squares will be 1 : 2.
Hence, option (d).