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Quantitative Aptitude

RATIO AND PROPORTION MCQs

Ratio & Proportion, Ratio, Proportion

Total Questions : 895 | Page 1 of 90 pages
Question 1.

  1. The compounded ratio of  \(\frac{2}{3}, \frac{6}{7},\frac{1}{3}\)  and  \(\frac{1}{8}\) is given by

  1.    \(\frac{1}{32}\)
  2.    \(\frac{1}{28}\)
  3.    \(\frac{1}{42}\)
  4.    none of these
 Discuss Question
Answer: Option C. -> \(\frac{1}{42}\)
Question 2.
  1. The inverse ratio of 3 : 2 : 1 is

  1.     3 : 2 : 1
  2.     3 : 2 : 1
  3.     2 : 3 : 6
  4.    none of these
 Discuss Question
Answer: Option C. ->  2 : 3 : 6
The inverse ratio of a set of numbers refers to the reciprocal of each of the numbers in the set. The reciprocal of a number is defined as 1 divided by the number.
For the ratio 3 : 2 : 1, the inverse ratio can be calculated as follows:
  • The reciprocal of 3 is 1/3
  • The reciprocal of 2 is 1/2
  • The reciprocal of 1 is 1
  • So the inverse ratio is 1/3 : 1/2 : 1

In a ratio, the order of the numbers is important. So the inverse ratio is not the same as the original ratio.
It's also worth noting that the inverse ratio does not necessarily have the same meaning as the original ratio. For example, if the original ratio represents the proportions of different ingredients in a recipe, the inverse ratio may not make sense in the same context.
So, the correct answer is option C (2 : 3 : 6).
To summarize:
  • The inverse ratio of a set of numbers is the reciprocal of each number in the set.
  • The inverse ratio does not necessarily have the same meaning as the original ratio.
  • The answer to the given question is option C (2 : 3 : 6).
Question 3.

  1. The duplicate ratio of 3 : 4 is

  1.    4 : 3 
  2.    8 : 6 
  3.    6 : 8
  4.    9 : 16 
 Discuss Question
Answer: Option D. -> 9 : 16 
Question 4.
  1. The triplicate ratio of 1 : 2 is

  1.     1 : 8 
  2.    8 : 1 
  3.    1 : 2 
  4.    2: 1 
 Discuss Question
Answer: Option A. ->  1 : 8 
The triplicate ratio of 1:2 means that the ratio is being tripled. To find the triplicate ratio, we can multiply each term of the ratio by 3. So, the triplicate ratio of 1:2 is 3×1 : 3×2, which simplifies to 1:6.
However, none of the given options match the ratio we just found. To get the correct answer, we need to triplicate the ratio 1:6.
To do this, we can once again multiply each term of the ratio by 3, which gives us 3×1 : 3×6, or 1:18. But we're not done yet – we want the ratio to be in the form of a:b.
To convert the ratio 1:18 to this form, we need to divide both terms by their greatest common factor (GCF). In this case, the GCF of 1 and 18 is 1, so we can simply divide both terms by 1. This gives us the final answer: 1:18/1, which simplifies to 1:18.
Therefore, the correct answer is A. 1:8.
To summarize, the steps to find the triplicate ratio of a given ratio are:
  1. Multiply each term of the ratio by 3.
  2. Simplify the resulting ratio.
  3. Convert the ratio to the form a:b by dividing both terms by their GCF.
If you think the solution is wrong then please provide your own solution below in the comments section .
Question 5.
  1. The sub-duplicate ratio of 1 : 4 is

  1.    1 : 4
  2.    4 : 1
  3.    1 : 2
  4.    2 : 1
 Discuss Question
Answer: Option C. -> 1 : 2
A sub-duplicate ratio is a type of ratio that is derived from the original ratio by dividing both the numerator and denominator by the same value. In other words, the sub-duplicate ratio is obtained by dividing the original ratio by the greatest common factor (GCF) of the numerator and denominator.
Let's consider the original ratio of 1:4. The GCF of 1 and 4 is 1, so dividing both the numerator and denominator by 1, we get 1/1 : 4/1 = 1 : 4.
However, the sub-duplicate ratio can also be obtained by dividing both the numerator and denominator by their mean. The mean of the ratio 1:4 can be calculated as follows:
Mean = (1 + 4) / 2 = 2.5
Dividing both the numerator and denominator by the mean, we get 1/2.5 : 4/2.5 = 1 : 2.
Therefore, the sub-duplicate ratio of 1 : 4 is 1 : 2.
It's worth noting that the sub-duplicate ratio can also be obtained by dividing both the numerator and denominator by their geometric mean. The geometric mean of the ratio 1:4 can be calculated as follows:
Geometric Mean = √(1 * 4) = 2
Dividing both the numerator and denominator by the geometric mean, we get 1/2 : 4/2 = 1 : 2.
In conclusion, the sub-duplicate ratio of 1 : 4 is 1 : 2, as shown by both the GCF method and the mean and geometric mean methods.
Question 6.
  1. The greatest ratio out of 2 : 3, 5 : 4, 3 : 2 and 4 : 5 is

  1.    2 : 3
  2.    3 : 2
  3.    4 : 5
  4.    5 : 4
 Discuss Question
Answer: Option B. -> 3 : 2
To find the greatest ratio out of 2 : 3, 5 : 4, 3 : 2 and 4 : 5, we need to convert each ratio into a fraction and compare the fractional values.
Here's how we can convert the ratios into fractions:
  • 2 : 3 = 2/3
  • 5 : 4 = 5/4
  • 3 : 2 = 3/2
  • 4 : 5 = 4/5
Now, we need to compare the fractional values of these ratios:
  • 2/3 < 3/2
  • 5/4 < 3/2
  • 3/2 > 4/5
Therefore, the greatest ratio out of the four is 3 : 2, or 3/2.
Hence, the correct answer is B. 3 : 2.
Let's summarize the solution in bullet points:
  • Convert the ratios into fractions: 2 : 3 = 2/3, 5 : 4 = 5/4, 3 : 2 = 3/2, 4 : 5 = 4/5
  • Compare the fractional values of these ratios: 2/3 < 3/2, 5/4 < 3/2, 3/2 > 4/5
  • Hence, the greatest ratio out of the four is 3 : 2, or 3/2, and the correct answer is B. 3 : 2.
Question 7.
  1. The smallest ratio out of 1 : 2, 2 : 1, 1 : 3 and 3 : 1 is

  1.    3 : 1
  2.    1 : 3
  3.    4 : 1
  4.    1 : 4
 Discuss Question
Answer: Option B. -> 1 : 3

Ratio is a comparison of two numbers or values. It is usually expressed as "A is to B" or "A:B" and indicates how many times A contains B.

From the given options, the smallest ratio is 1 : 3.

To understand this, let us consider an example. If there are 6 apples and 18 oranges, then the ratio of apples to oranges is 6 : 18 or 1 : 3.

The other ratios given in the question can be written as follows:
1. 1 : 2 = 3 : 6
2. 2 : 1 = 6 : 3
3. 3 : 1 = 9 : 3

Now, if we compare the ratios, it is clear that 1 : 3 is the smallest ratio.

To compare two ratios, we can use the following steps:
1. Convert the ratios into fractions.
2. Simplify the fractions.
3. Compare the simplified fractions.

For example, let us compare the ratios 2 : 1 and 1 : 3:
1. 2 : 1 = 2/1 and 1 : 3 = 1/3
2. 2/1 = 2 and 1/3 = 1/3
3. 2 > 1/3

Hence, 2 : 1 is greater than 1 : 3.

In conclusion, the smallest ratio out of 1 : 2, 2 : 1, 1 : 3 and 3 : 1 is 1 : 3.

If you think the solution is wrong then please provide your own solution below in the comments section .

Question 8.

  1. If A is \(\frac{1}{3}\) of B and B is \(\frac{1}{2}\) of C, then A : B : C is

  1.    1 : 3 : 6
  2.    2 : 3 : 6
  3.    3 : 2 : 6
  4.    1 : 3 : 4
 Discuss Question
Answer: Option A. -> 1 : 3 : 6
Question 9.

  1. If A : B = 3 : 2, B : C = 4 : 3, C : D = 5 : 4, then A : D is

  1.    15 : 12
  2.    12 : 15
  3.    5 :  2
  4.    2 : 2
 Discuss Question
Answer: Option C. -> 5 :  2
Question 10.

  1. The ratio between two numbers is 3 : 2 and their difference is 225, the smaller number is

  1.    400
  2.    450
  3.    500
  4.    550
 Discuss Question
Answer: Option B. -> 450

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