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Smera mixes a 20% alcohol solution and a 30% alcohol solution in the respective ratio of c : d. The new solution thus obtained is mixed with an equal quantity of a 60% alcohol solution to obtain a 42% alcohol solution. Which among the following represents the ratio c : d?
  • a)
    4 : 1
  • b)
    3 : 2
  • c)
    5 : 2
  • d)
    Data insufficient
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Smera mixes a 20% alcohol solution and a 30% alcohol solution in the r...
Let Smera mix c litres of the 20% solution and d litres of the 30% solution.
Thus, the following equation can be set up:
   ► 20c + 30d + 60(c + d) = 42 x 2(c + d) Or, 3d = 2c Or, c : d = 3 : 2
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Smera mixes a 20% alcohol solution and a 30% alcohol solution in the r...
Let's assume that Smera mixes c liters of the 20% alcohol solution and d liters of the 30% alcohol solution.

First Mixture: 20% alcohol solution and 30% alcohol solution
The total quantity of the first mixture is c + d liters.
The total alcohol content in the first mixture can be calculated as 20% of c + 30% of d.

Second Mixture: First mixture and 60% alcohol solution
The total quantity of the second mixture is equal to the total quantity of the first mixture, which is c + d liters.
The total alcohol content in the second mixture can be calculated as 42% of (c + d).

To find the ratio c:d, we need to find the values of c and d that satisfy the given conditions.

Algebraic Equation 1: Total alcohol content in the first mixture
0.2c + 0.3d = (0.2c + 0.3d)

Algebraic Equation 2: Total alcohol content in the second mixture
0.42(c + d) = 0.2c + 0.3d + 0.6(c + d)

Now, let's simplify the second equation:

0.42c + 0.42d = 0.2c + 0.3d + 0.6c + 0.6d
0.42c + 0.42d = 0.8c + 0.9d

Subtracting 0.8c and 0.9d from both sides:

0.42c - 0.8c + 0.42d - 0.9d = 0
-0.38c - 0.48d = 0

Dividing through by -0.38:

c + 1.26d = 0

Since the equation c + 1.26d = 0 has infinite solutions, we have an indeterminate system. This means that the given information is not sufficient to determine the ratio c:d.

Hence, the correct answer is option D) Data insufficient.
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Smera mixes a 20% alcohol solution and a 30% alcohol solution in the respective ratio of c : d. The new solution thus obtained is mixed with an equalquantity of a 60% alcohol solution to obtain a 42% alcohol solution. Which among the following represents the ratio c : d?a)4 : 1b)3 : 2c)5 : 2d)Data insufficientCorrect answer is option 'B'. Can you explain this answer?
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