Ratio and proportion - Aptitude Questions

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Introduction:

In Nithra Jobs site, we has given ratio and proportion aptitude questions and answers for preparing competitive exams and interviews. Ratio and Proportion aptitude tricks are essential mathematical concepts that provide a framework for comparing and relating quantities. These Ratio and Proportion aptitude concepts play a crucial role in solving problems related to percentages, proportions, scaling, and more. Understanding and applying ratio and proportion aptitude formula effectively is a valuable skill that can greatly enhance your problem-solving abilities, mathematical reasoning, and analytical thinking.

Formulas:

1. Ratio:

The ratio of two quantities a and b in the same units, is the fraction a/b and we write it as a : b. In the ratio a : b, we call a as the first term or antecedent and b, the second term or consequent.

Eg. The ratio 5 : 9 represents 5/9 with antecedent = 5, consequent = 9.

Rule: The multiplication or division of each term of a ratio by the same non-zero number does not affect the ratio.

Eg. 4 : 5 = 8 : 10 = 12 : 15. Also, 4 : 6 = 2 : 3.

2. Proportion:

The equality of two ratios is called proportion.

If a : b = c : d, we write a : b :: c : d and we say that a, b, c, d are in proportion.

Here a and d are called extremes, while b and c are called mean terms.

Product of means = Product of extremes. Thus, a : b :: c : d ⇒ (b x c) = (a x d).

3. Fourth Proportional:

If a : b = c : d, then d is called the fourth proportional to a, b, c.

Third Proportional:

a : b = c : d, then c is called the third proportion to a and b.

4. Comparison of Ratios:

We say that (a : b) > (c : d) ⇒ a / b > c / d.

Compounded Ratio:

The compounded ratio of the ratios: (a : b), (c : d), (e : f) is (ace : bdf).

5. Duplicate Ratios:

Duplicate ratio of (a : b) is (a2 : b2).

Sub-duplicate ratio of (a : b) is (√a : √b).

Triplicate ratio of (a : b) is (a3 : b3).

Sub-triplicate ratio of (a : b) is (a1/3 : b1/3).

If a/b = c/d, then (a + b) / (a - b) = (c + d) / (c - d) [component do and dividend do]

6. Variations:

We say that x is directly proportional to y, if x = ky for some constant k and we write, x = y.

We say that x is inversely proportional to y, if xy = k for some constant k and we write, x = 1/y.

Solved Problems

1. 1 : 3 = 1 (2/3) : x. The value of x is?

Answer: 5

Explanation:

x * 1 = 3 * 5 / 3

x = 5

2. What number has a 5 : 1 ratio to the number 10?

Answer: 50

Explanation:

5 : 1 = x : 10

5 / 1 = x / 10

x = 5 * 10

x = 50

3. If a : b = 7 : 5, b : c = 9 : 11, find a : b : c?

Answer: 63: 45: 55

Explanation:

LCM of 7 and 9 is 63.

LCM of 5 and 11 is 55.

Multiply each ratio by the LCM of its two terms.

a : b = 7 x 63 : 5 x 63 = 441 : 315

b : c = 9 x 55 : 11 x 55 = 495 : 555

Combine the two ratios.

a : b : c = 441 : 315 : 495

Divide each term in the ratio by 9, we get 63 : 45 : 55

a : b : c = 63 : 45 : 55

4. If a : b = 3 : 4, b : c = 7 : 9, c : d = 5 : 7, find a : d?

Answer: 5/12

Explanation:

a : d = a : b * b : c * c : d

a / d = ( 3 / 4 ) * ( 7 / 9 ) * ( 5 / 7 )

= 5 / 12

5. The inverse ratio of 3 : 2 : 1 is?

Answer: 2 : 3 : 6

Explanation:

The inverse of 3 is = 1/3

The inverse of 2 is = 1/2

The inverse of 1 is = 1

1 / 3 : 1 / 2 : 1 / 1 = 2 : 3 : 6

Conclusion

With the right knowledge practicing problems on ratio and proportion aptitude, you can confidently tackle quantitative aptitude questions and impress interviewers with your logical reasoning skills. Nithra Jobs site is there to help you by providing the ratio and proportion problems with formulas that strengthen your understanding of ratio and proportion. Let Nithra Jobs be your guide on this journey towards achieving your career aspirations.