Logical Reasoning

Math Puzzles

Hard

Each of the bottles mentioned in this question contains 50 ml of liquid. The liquid in any bottle can be 100% pure content (P) or can have certain amount of impurity (I). Visually it is not possible to distinguish between P and I. There is a testing device which detects impurity, as long as the percentage of impurity in the content tested is 10% or more.

For example, suppose bottle 1 contains only P, and bottle 2 contains 80% P and 20% I. If content from bottle 1 is tested, it will be found out that it contains only P. If content of bottle 2is tested, the test will reveal that it contains some amount of I. If 10 ml of content from bottle 1is mixed with 20 ml content from bottle 2, the test will show that the mixture has impurity, and hence we can conclude that at least one of the two bottles has I. However, if 10 ml of content from bottle 1 is mixed with 5 ml of content from bottle 2. the test will not detect any impurity in the resultant mixture.

There are four bottles. Each bottle is known to contain only P or only I. They will be considered to be “collectively ready for despatch” if all of them contain only P. In minimum how many tests, is it possible to ascertain whether these four bottles are “collectively ready for despatch”?.

Entered answer:

✅ Correct Answer: 1

Slide 1/2

Understanding the set :-

This is a mixture and allegations set :

Mixtures and allegations is mixing two things with different prices or strengths to get a mixture with a middle value.

For eg -

Milk costs ₹6 per litre, water is free (₹0).

We want a mixture costing ₹4 per litre.

Step 1: Values → High = 6, Low = 0, Mean = 4

Step 2: Subtract diagonally:

6 - 4 = 2

4 - 0 = 4

Ratio = 2 : 4 = 1 : 2

So, milk : water = 1 : 2

In this question there are 50 ml bottles

also, iquid in any bottle can be 100% pure content (P) or can have certain amount of impurity (I).

There is a testing device which detects impurity, but that detects, only if impurity is more then 10%.

Now, the set will be solved according to each question separately.

The bottles contain either P(pure) or I(impure).

The possible cases here are :

1- (P, P, P, P),

2-(P,P,P,I),

3-(P,P,I,I),

4-(P,I,I,I),

5-(I,I,I,I).

In the first case if all the four solutions are pure then taking equal volumes of all the four bottles will get the result to dispatch or not to dispatch.

In the second case if 3 bottles are pure and one impure taking equal volumes of all four bottles and testings will confirm the impurity and hence cannot be dispatched.

In the third case if 2 bottles are pure and two are impure taking equal volumes of all four bottles and testing will confirm the impurity and hence cannot be dispatched.

In the fourth case when only one bottle is pure taking equal volumes of all four bottles will confirm the impurity and hence cannot be dispatched.

In the fifth case if all four bottles are impure taking equal volumes of the four bottles will confirm the impurity and hence cannot be dispatched.

In all the cases a single test is enough to determine if the lot is to be dispatched or not.

Question 17

5 ml of content from bottle A is mixed with 5 ml of content from bottle B. The resultant mixture, when tested, detects the presence of I. If it is known that bottle A contains only P, what BEST can be concluded about the volume of I in bottle B?

Question 19

There are four bottles. It is known that three of these bottles contain only P, while the remaining one contains 80% P and 20% I. What is the minimum number of tests required to definitely identify the bottle containing some amount of I?

Question 20

There are four bottles. It is known that either one or two of these bottles contain(s)only P, while the remaining ones contain 85% P and 15% I. What is the minimum number of tests required to ascertain the exact number of bottles containing only P?

There are four bottles. Each bottle is known to contain only P or only I. They will be considered to be “collectively ready for despatch” if all of them contain only P. In minimum how many tests, is it possible to ascertain whether these four bottles are “collectively ready for despatch”?.

Solution

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