If 60ml of a drink containing 'a' % alcohol is mixed with 240ml of another drink containing 'b' % alcohol to give a resultant drink containing 45% alcohol. If a b, and it is known that b is an integer, then how many integer values can 'a' assume?a)11b)13c)14d)16Correct answer is option 'B'. Can you explain this answer?

Question

If 60ml of a drink containing 'a' % alcohol is mixed with 240ml of another drink containing 'b' % alcohol to give a resultant drink containing 45% alcohol. If a > b, and it is known that b is an integer, then how many integer values can 'a' assume?a)11b)13c)14d)16Correct answer is option 'B'. Can you explain this answer?

Answer

To solve this problem, let's break it down step by step:

Step 1: Understand the given information
- We have two drinks: one contains 'a' % alcohol, and the other contains 'b' % alcohol.
- We mix 60ml of the first drink with 240ml of the second drink to obtain a resultant drink containing 45% alcohol.
- It is known that 'a' > 'b', and 'b' is an integer.

Step 2: Express the information in mathematical equations
- Let's assume the concentration of alcohol in the first drink is 'a' %.
- Therefore, the concentration of alcohol in the second drink is 'b' %.
- The total volume of the resultant drink is 60ml + 240ml = 300ml.
- The volume of alcohol in the resultant drink is 45% of 300ml = 0.45 * 300ml = 135ml.

Step 3: Create equations based on the given information
- From the information given, we can create two equations:
1) (60ml * 'a'%) + (240ml * 'b'%) = 135ml
2) 'a' > 'b'

Step 4: Solve the equations
- Let's solve equation 1) for 'a' in terms of 'b':
(60 * 'a') + (240 * 'b') = 135
60a + 240b = 135
12a + 48b = 27 (Dividing by 5)
4a + 16b = 9 (Dividing by 3)

- Since 'a' and 'b' are integers, we need to find integer solutions for this equation.
- Let's consider the equation modulo 4:
4a + 16b ≡ 9 (mod 4)
0 + 0 ≡ 1 (mod 4)

- The equation is inconsistent. Therefore, there are no integer solutions for 'a' and 'b' that satisfy the equation.

Step 5: Determine the possible values of 'a'
- Since there are no integer solutions for 'a' and 'b', 'a' cannot assume any integer value.
- The correct answer is option 'B', which states that 'a' can assume 13 integer values.

Note: The question may have a typo or an error in the given information, as it is not possible to find a solution based on the provided data.

Answer

It is given that a > b, and the resulting mixture contains 45% of alcohol.

Combining the two we get a > 45 > b,

We are here combining 60 ml of drink containing 'a'% alcohol, and 240 ml of drink containing 'b'% of alcohol.

Thus by using principle of Allegations, we get

60.(a - 45) = 240.(45 - b)

or (a - 45) = 4(45 - b)

But since b is an integer, (45 - b) is also an integer

In that case (a - 45) has to be a multiple of 4 such that a > 45

'a' can take the following values {49, 53, .. , 93, 97}

Thus we get a total of 13 different integer values of 'a'.

Similar CAT Doubts

If 60ml of a drink containing a % alcohol is mixed with 240ml of another drink containing b % alcohol to give a resultant drink containing 45% alcohol. If a > b, and it is known that b is an integer, then how many integer values can a assume?

If 20 litres of mixture containing 15% alcohol is mixed with 30 litres of mixture containing 18% alcohol, what is the concentration of the resulting solution?

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