How to prepare Ratio and Proportion?

Before we get into the details, let us revisit the definition of ratio and proportion:

On the other hand, Proportion is a statement that two ratios are similar, i,e. when two ratios are equal then they make a proportion. For instance, if a/b = c/d, then a, b, c, and d are in proportion. This can also be represented as a:b :: c:d, where a and d are known as Extremes, while b and c are called Means. It is also worth remembering that the product of mean shall always be equal to the product of extremes, i.e. ad = bc.

Having understood the definitions, let us look at different types of questions on Ratio and Proportion.

Example 1:

Given that a:b = 2:3 and b:c = 5:7, compute a:b:c

Solution: This is one of the easiest types of questions to solve. If you observe, there is a common factor in both the ratios, i.e. “b”, as it is appearing in both the ratios. In the first ratio, the value of b is 3, while in the second it is 5. You can follow the following steps to solve this:

Step 1: Take the LCM of b, i.e. 3 and 5. In this case, it shall be 15 (i.e. 3 x 5, since both are prime numbers).

Step 2: Convert both ratios so that it has the same number, i.e. 15. For instance, in the first ratio, a:b = 2:3, multiply both the numerator and denominator with 5 to get 10:15. In the second ratio, multiply the ratio with 3 to get b:c = 15:21.

Step 3: After the ratios are converted, you will get, a:b = 10:15 and b:c = 15:21. Therefore, a:b:c = 10:15:21, since 15 is common in both ratios.

Hence, your answer will be 10:15:21.

Example 2:

A, B and C entered into a partnership with a profit-sharing ratio of 3:4:5. At the end of the year, their business generated a profit of Rs 24000. How much profit did each of them receive?

Solution: This is also a straightforward question, and will take a few seconds only to solve by following the below-mentioned steps.

Step 1: Sum the total number of parts, i.e. 3+4+5 = 12

Step 2: Calculate the share of each of the partners:

A = 3/12 x 24000 = 6000

B = 4/12 x 24000 = 8000

C = 5/12 x 24000 = 10000

Hence, the answer is A gets 6000, B gets 8000 and C gets 10000

Example 3:

A, B and C entered into a partnership with a profit-sharing ratio such that A will get 2/9^th of B’s share, while C will get 3/4^th of A’s share. At the end of the year, their business generated a profit of Rs 6250. How much profit did each of them receive?

Solution: This is also a straightforward question, and will take a few seconds only to solve by following the below-mentioned steps.

Step 1: Let us first write down the proportion, A:B = 2:9 and C:A = 3:4

Step 2: Take the LCM of A, i.e. 2 and 4. In this case, it shall be 4.

Step 3: Convert both ratios so that it has the same number, i.e. 4. For instance, in the first ratio, A:B = 2:9, multiply both the numerator and denominator with 2 to get 4:18. In the second ratio, multiply the ratio with 1 to get C:A = 3:4.

Step 4: After the ratios are converted, you will get, A:B= 4:18 and C:A = 3:4. Therefore, A:B:C = 4:18:3.

Step 5: Sum the total number of parts, i.e. 4+18+3= 25

Step 6: Calculate the share of each of the partners:

A = 4/25 x 6250 = 1000

B = 18/25 x 6250 = 4500

C = 3/25 x 6250 = 750

Hence, the answer is A gets 1000, B gets 4500 and C gets 750

Example 4:

The sum of the ages of A and B is 59 years. Further, A is 4 years older to C. The ratio of ages of B:C is 4:7. Find the current age of A. Also, calculate A’s age 5 years back.

Solution: You may follow the below-mentioned steps to solve the question.

Step 1: We know A + B = 59. Also, because A is 4 years older than C, the ratio of B:C shall be 55 (i.e. 59 – 4).

Step 2: Since the ratio of B:C is 4:7, hence, solve this to get the age of B and C. For this, sum the total number of parts, i.e. 4+7 = 11, and then equate it with 55. You will get 1 = 5

Step 3: Calculate the age of B and C.

B = 4 x 5 = 20

C = 7 x 5 = 35

Step 4: Now calculate the current age of A:

A + B = 59

A = 59 – 20 = 39

Step 5: Subtract 5 from the current age of A to get A’s age 5 years ago, i.e. 39 – 5 = 34 years

Hence, the current age of A is 39 years, while 5 years back he was 34 years old.

Example 5:

Five years ago, the age of A and B was in the ratio of 6:7. Seven years later, A’s age will 10% less than B’s age. Find the age of B after 10 years.

Solution: In this question, some basic understanding of percentages will also be applied. You may follow the below-mentioned steps to solve the question.

Step 1: Let B’s age after 7 years be X.

Step 2: If B’s age after 7 years is X, then A’s age will be X – (1/10)X = (9/10)X

Step 3: Now that we know the age of A and B, let us put it in the form of a ratio, i.e. A:B = (9/10)X : X = 9:10

Step 4: Five years ago, the ratio of age of A:B was 6:7, while after five years it is 9:10. The difference between the years is 12 years, i.e.

3 = 12,

1 = 4

Step 5: Calculate the age of A and B using the above value:

B’s age after 7 years will be: 10 x 4 = 40 years

B’s age after 10 years will be: 40 + 3 = 43 years

Hence, B’s age after 10 years will be 43 years

We hope this article will be helpful in your preparation and wish you all the best for your exam.

Happy learning!