Hello and welcome to exampundit . Here is a set of Data Interpretation Quiz for RBI Grade B Phase I.
Rahul 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 Rahul.
1. Rahul should not test if the number of bad widgets in the lot is:
(a) less than 100
(b) more than 200
(c) between 120 & 190
(d) Cannot be found out
2. If there are 120 defective widgets in the lot, Rahul:
(a) should either use Test I or not test.
(b) should either use Test II or not test.
(c) should use Test I or Test II.
(d) should use Test I only.
3. If the number of defective widgets in the lot is between 200 and 400, Rahul:
(a) may use Test I or Test II
(b) should use Test I only.
(c) should use Test II only
(d) cannot decide.
4. If Rahul is told that the lot has 160 defective widgets, he should:
(a) use Test I only
(b) use Test II only.
(c) do no testing.
(d) either use Test I or do not test.
5. If there are 200 defective widgets in the lot, Rahul:
(a) may use either Test I or Test II
(b) should use Test I or not use any test
(c) should use Test II or not use any test.
(d) cannot decide.
Total number of batches = 1000
Let p be the total number of bad widgets
Therefore the total number of good ones will be (1000 –p).
On test I his total cost will be = Rs.2 (1000) + 25 x 0.8p + 50 x 0.2p
On test 2 his total cost will be = Rs. 3(1000) + 25 x p
Now, it will be worth testing if the cost of testing is less than the cost of penalty levied on the defective pieces. Let us check all the choices:
Above 100 defectives cost is cheaper than the penalty.
But for 100 defectives the cost of penalty is the same as that for testing. Therefore we come to this conclusion that below 100 defectives, the penalty will be less than the cost of testing and hence it is not worth testing.
If there are 120 widgets, he should go for test I as it is cheaper.
From the table we can say that if the number of defectives is between 200 & 400, he should go for Test II as it is cheaper.
In case of 160 defectives he should use test I as it is cheaper.
As the cost of both the Tests is same = Rs.8000.
Prakash may use either Test I or Test II for 200 widgets