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CAT 1991 — QA Question 6

PercentageEasy
Passage / Data

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.

Prakash should not test if the number of bad widgets in the lot is:

Answer & solution

Correct answer: less than 100

  • less than 100

  • B

    more than 200

  • C

    between 120 & 190

  • D

    Cannot be found out.

Solution

Let the number of defective widgets be ‘x’.

Cost to Prakash if he does not use any test = 50x

Cost to Prakash if he uses test 1 = 2 × 1000 + 4x5× 25 + x5× 50 = 2000 + 30x

Cost to Prakash if he uses test 2 = 3000 + 25x

Prakash should not test when 50x ≤ (2000 + 30x) and (3000 + 25x)

50x ≤ (2000 + 30x) and 50x ≤ (3000 + 25x)

20x ≤ 2000 and 25x ≤ 3000

x ≤ 100 and x ≤ 120

x ≤ 100 

Prakash should use test 1 when test 1 is cheaper than test 2

3000 + 25x ≥ 2000 + 30x

5x ≤ 1000

x ≤ 200

For x ≥ 200 he can use test 2.

Below 100, no test would be cheaper.

Hence, option (a).

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CAT 1991 QA Q6: Prakash should not test if the number of bad widgets in the lot is: — Solution | TheCATExam